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National Bureau of Standards

Library, E-01 Admin. Bldg.

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*°»CAU 0« •

OCT 6 1981

J911W NBS TECHNICAL NOTE 1 030

U.S. DEPARTMENT OF COMMERCE /National Bureau of Standards
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress on March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and

the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

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physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

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provides engineering measurement traceability services; develops test methods and proposes

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research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing the Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and

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'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Washington, DC 20234.

2 Some divisions within the center are located at Boulder, CO 80303.
MATIOMA1, BTOUEAO

OF tfTANSABDS

L1PBART

Four Mathematical Models jocose.

for the Prediction qc

of LNG Densities

Robert D. McCarty

Thermophysical Properties Division

National Engineering Laboratory

National Bureau of Standards

Boulder. Colorado 80303

rf

i c/ W? \

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Jordan J. Baruch, Assistant Secretary for Productivity, Technology and Innovation

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued December 1980
NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 1030

Nat. Bur. Stand. (U.S.), Tech. Note 1030, 84 pages (Dec. 1980)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1980

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Price $4.00

(Add 25 percent additional for other than U.S. mailing)
CONTENTS

Page

Abstract 1

1. INTRODUCTION 1

2. EXTENDED CORRESPONDING STATES 3

3. A HARD SPHERE METHOD 6

4. A REVISED KLOSEK AND MCKINLEY METHOD 11

5. THE CELL MODEL 13

6. USE OF THE METHODS 15

7. CONCLUSIONS 19

8. REFERENCES 20

Appendix A. Experimental Data 24

Appendix B. Computer Program and Equation Parameters for the

Extended Corresponding States Model 39

Appendix C. Computer Program and Equation Parameters for the

Hard Sphere Model 46

Appendix D. Computer Program and Parameters for the Revised

Klosek and McKinley Model 50

Appendix E. Computer Program for the Cell Model 54

Appendix F. Computer Programs 55

in

FOUR MATHEMATICAL MODELS FOR THE PREDICTION OF LNG DENSITIES*

Robert D. McCarty

Thermophysical Properties Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

Four mathematical models of the equation of state for LNG like

mixtures are presented. The four models include an extended

corresponding states model, a cell model, a hard sphere model and a revised Klosek and McKinley model. Each of the models has been

optimized to the same experimental data set which included data for

pure nitrogen, methane, ethane, propane, iso and normal butane, iso and

normal pentane and mixtures thereof. For LNG like mixtures (mixtures

of the orthobaric liquid state at temperatures of 120 K or less and

containing at least 60% methane, less than 4% nitrogen, less than 4%

each of iso and normal butane and less than 2% total of iso and normal

pentane), all of the models are estimated to predict densities to within

0.1% of the true value. The revised Klosek and McKinley model is valid

only for mixtures within the range of temperature and composition

specified above while the other three models are valid for a broader

range of pressure, temperature and composition. The experimental PVTx

data set used in the optimization together with comparisons are given

and listings of computer programs for each of the models are included.

Key words: Cell model; comparisons; computer programs; corresponding states;

equation of state; hard sphere; LNG; mixtures; PVTx data; revised Klosek and

McKinley.

1. INTRODUCTION

The purpose of this report is to present in final form the four mathematical

models which were optimized to the experimentally determined orthobaric liquid

This work was carried out at the National Bureau of Standards under the

sponsorship of British Gas Corp., Chicago Bridge and Iron Co., Columbia Gas

Service Corp., Distrigas Corp., Easco Gas LNG, Inc., El Paso Natural Gas, Gaz de

France, Marathon Oil Co., Mobil Oil Corp., Natural Gas Pipeline Co., Phillips

Petroleum Co., Shell International Gas, Ltd., Sonatrach, Southern California Gas

Co., Tennessee Gas Pipeline, Texas Eastern Transmission Co., Tokyo Gas Co., Ltd.,

and Transcontinental Gas Pipe Line Corp., through a grant administered by the

American Gas Association, Inc.
PVTx data of Miller and Hiza [25], Haynes and Hiza [12], Haynes, et al . [11],

Hiza, et al. [14], Hiza and Haynes [15] and Haynes [9], Interim results of the

project have been reported by Haynes, et al . [13] and by McCarty [23]. The

models reported in these two interim publications differ only slightly from those

presented here. A companion archival document, McCarty [24] with the same

results but in much less detail has been submitted to the Journal of Chemical

Thermodynamics. The intent of the documentation here is more in the vein of a

user's handbook. The above experimental data are for the liquid phase of

nitrogen, methane, ethane, propane, normal and isobutane and various mixtures

thereof.

The goal of the project (the project included the above referenced experimental work) was to produce one or more computer models which would predict the

density of LNG to within 0.1% of the true value from a knowledge of the

temperature, pressure and composition of the LNG. At the beginning of this study

LNG was defined as mixtures of the above components (N«, CH«, C^Hg, C

3

Hg

,

n and iC,H,

Q

) and only the saturated liquid between 95 - 150 K was to be

considered. Near the end of the project n and iC

5 H,« were added to the list of

allowable components but no experimental PVTx of pure n and iCrH, or binary

systems containing n and iC

5

H, 2 were measured as part of the project. The

inclusion of these two components is based on data from Orrit, et al . [29] and

Orrit, et al . [30].

Four models were considered: the extended corresponding states model, a

hard sphere model, a cell model and a Revised Klosek and McKinley model. With

the exception of the Revised Klosek and McKinley model only pure fluid and binary

system data were used to optimize the models. In the case of the Revised Klosek

and McKinley model multi component PVTx data were used in the optimization

process.
Over a normal range of LNG composition and temperature all four of the

models predict densities which agree to within 0.1% of experiment. This is true

of all of the experimental PVTx measurements on LNG like mixtures made as part of

this project.

No equation or mathematical model based on experimental data can be more

accurate than the original data and therefore the extent to which the original

goal of 0.1% accuracy has been met depends entirely upon the accuracy of the

experimental data referenced above.

There is no reason to doubt the experimental data and therefore there is

every reason to believe that the goal of the project has been achieved.

2. EXTENDED CORRESPONDING STATES

The thermodynamic equations for the extended corresponding states method are

developed in a paper by Rowlinson and Watson [35] and only a very brief

description will be given here. Leach [20] developed transformation functions

for hydrocarbons which are called shape factor functions. Mollerup [27] and

Mollerup and Rowlinson [26] combined the earlier work with the equation of state

for methane by Goodwin [8] to produce a computer program to calculate the density

of LNG mixtures, which was further modified by Mollerup [28].

The computer program in Appendix F for the calculation of LNG densities

based on the extended corresponding states method is an extensive revision of the

Mollerup program. Earlier revisions were reported by McCarty [23] and Haynes,

Hiza and McCarty [13].

The extended corresponding states method is defined by the following

equations:

Ip.Tl - Z [Ph 1i;0/f ii>o> T/f

ji)0 ] (1)
G i^T] - fii,o G

o[ph ii,o/f

ii,o' T/fii > o

]

- RT

^

h

ii > o»

< 2 >

where Z is the compressibility factor, G is the Gibbs free energy, P is pressure

and T is temperature. The subscript o denotes the reference fluid and the

subscript i denotes the fluid for which properties are to be obtained via the

equation of state for the reference fluid and the transformation functions

f . . and h . . . The double subscript ii is introduced now to allow extension

n,o n ,o

r

of the method to mixtures. The two defining eqs (1) and (2) are necessary since

there are two transformation functions. In this case the equation of state for

methane by McCarty [22] was chosen for the reference fluid. During the course of

the study it was necessary to modify the equation of state by McCarty [22] to

give a realistic vapor liquid phase boundary down to a temperature of 43 K. This

modification was necessary to accommodate the very low reduced temperatures of

the heavier hydrocarbons and was accomplished without changing the performance of

the equation of state above the triple point of methane. The equation of state

is given in Appendix B.

The f. . „ and h.. n are defined as n ,o n ,o

fii,o < T

ii

/TC

o>

9ii,o ( W (3)

and

h ii,o < V ii,c/V

o> *ii,o <VV < 4 >

where

9 ii,o

= X + {w

i " wo )[nl " n 2

* n \

+ (n

3

" W.Wr. • n 5 )] (5 >

and
z

c n,o z

cI

[l + (w, - w )[n

6

(V r . - n

?

) - n 8

(V r

, - ng

) «n T ]] (6)

i

The V and T are reduced temperature and volume, (i.e., T = T/T .

. and

r

i ri i

V = V/v9 . ) each fluid requires a unique w. which was estimated using pure fluid

experimental data. A single set of the n

.

' s are used for all fluids. The n.'s

were estimated using all of the pure fluid experimental data from this study. The

1 II. is the ratio of the compressibility factors (Z = P CV /RT ) at the critical

point. The parameters n. , n., w. and Z.. are given in Appendix B. All of

these parameters were estimated using the experimental PVT data set from this

laboratory and least squares estimation techniques.

The extension of the above to mixtures is now accomplished by the following

application of the following combining rules:

h

x,o ? f

Vj h ij,o < 7 >

f

x,o \o - £

f

Vi fij,o h ij,o W

f- • = K- (f-. f-. ) 1/2

(9) iJ,o %ij v n,o jj,o ; KV >

h n ri h l/3 , 1 .1/3 x3 (

. n. h

ij,o " *4j (? h ii,o

+

2

hjj,o ) (10)

The 5.. and the r\.. are binary interaction parameters determined by least

squares from the PVTx data for binary mixtures. These parameters are given in

Appendix B.
This method works quite well as may be seen in the comparisons in

Appendix A. It has indeed reproduced all of the present experimental data set to

within + 0.1% except for 14 out of a total of 285 experimental data points. Of

these 14 points, 11 are judged to have an uncertainty greater than 0.1%.

Figure 1 presents the deviations between the calculated and experimental

densities for these 14 points. Appendix A contains comparisons of calculated and

experimental densities for the entire data set. This is the best performance of

the four models presented here. No pressure, temperature or composition

restrictions have been placed on this model.

In the interim publications by McCarty [23] and Haynes, Hiza and

McCarty [13] some doubt about the accuracy of the calculated densities was

expressed because of the disagreement with a few binary and multicomponent

systems containing methane and butane. This disagreement has since been resolved

by additional measurements (Haynes [9], Haynes [10] and Miller and Hiza [25] on

some of the systems which agree with the predictions of the model but disagree

with the previous measurements. The net result of the new measurements is a \/ery

slight change in binary interaction coefficients of the methane-butane and

nitrogen-butane system. These changes have no practical effect on LNG like

mixtures where the concentrations of N~ , i'C.H^q and nC

4

H,

Q are individually

less than 5%. In other words either the models presented here or those in the

interim publications may be used to predict the density of a LNG like mixture to

within 0.1% of the true density.

3. A HARD SPHERE METHOD

The model of Rodosevich and Miller [33] is one of many modifications of the

Longuet-Higgins and Widom [21] model, and was chosen to be included in this study
as a representative example of the application of the hard sphere equation of

state concept to the correlation of PVTx data. The equation of state by

Rodosevich and Miller [33] is

PV

RT

i + y + .y

(i - y)

3 RTV

(11)

where the y = b/4V and a, b, and c are adjustable parameters, P is pressure, V is

specific volume, T is temperature and R is the gas constant. The equation is

applied to mixtures by assuming the one-fluid theory and applying the following

combining rules.

= E E a,, x.x,. (12) m

J ij i J

b„ = E E b . . x . x

.

m

i J ij i J

= E E c. . x.

i j

ij i j

The mixing rules are:

b. . =

ij

rb 1/3

+ b

1/3

_U 0J_ (i . i

\ 2 u hy

-i 3

ij =( aii a ii)

1/2

b-.b-.

1/2

(1 kij )

(13)

(14)

(15)

(16)

ij

c . . + c .

.

(17)

The parameters j.. and k.. are in this case the binary interaction

parameters. The a's, b's, c's, j^'s and k..'s are given in Appendix B. The

excess volume is now calculated using the equation of state and
V

E

- V„- ViXi (18)

where V miand the V. are calculated via the eqs^ 11 through 17 and then

Vm

= V.x. + V

E (19)

where the VV is from eq (18) and the V. are from experimental data. The

values of V. in this case were calculated from the equations for the liquid

density of the pure fluids given in Appendix C.

The above equations are those of Rodosevich and Miller [33] and Rodosevich

[34] and only the j. . 's and k.-'s have been revised on the basis of the

i j i j

present new data set, and only binary systems data were used to estimate via

least squares the j - -

* s and k. • 's.

As the method is used here it is an excess volume method, and consequently

when the temperature of the mixture approaches the critical temperature of one of

the component fluids, the method fails. Since the critical temperature of

nitrogen is about 126 K, this method should not be used for mixtures containing

nitrogen at temperatures above 120 K. Eliminating the data points for mixtures

which contain nitrogen at temperatures above 120 K reduces the set from 285 to

251 PVTx points. Figure 2 is a percentage deviation plot containing all of the

data points from the set of 251 for which densities calculated by the hard sphere

method differ from the experimental density by more than 0.1%. Two things are

readily seen in comparing figs. 1 and 2; first, even though total number of

points has been reduced in the comparison set, the number of points for which

deviations exceed 0.1% in the hard sphere comparison, fig. 2, is far more than

for the extended corresponding states comparison, fig. 1. Second, the hard

sphere method becomes more uncertain for all mixtures, regardless of components

as the temperature exceeds 115 K.
+-1—

<

m + X

•Hs

QJ : z z z CD a

*•* + > <3 —

CO *»(0

i—

i

in vD <n 00

.—

1

on vO m

+

0) u c 3

MM 4-1 TO X : : : : ~ C OH •HB —

o

a + a < o >

CO

CD +

t_

k.o - o +

+ ao

1

< -

<

o

o

CO

o

CM

UJ

oc<

OC

UJ

CL

UJ

Io

M

O o

I AiiSNaa ni NOiiviAaa %

T3

QJ

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CO 4-1 !-H CO 3 73 O 0) .H X in

CO H 00 O CM *3 • s T3

CO O • XI <

rH 4-1 CO o> X

4-1 e •H 3 T3

a) co 3

B 0) QJ •H 4J a

M CO a

CU 4-1 <

a W

X 3

<u 603

•H c •H CO

ai T3 4-1 cu c 3

3 o •H

4-1 a O

01 CO a

^3 0)

J-l CO

e^? J-i 4J

.—

i

o CO

• u T3 o

T3 01 s (U x

CO -a 4-> ,3 s

4-J 0) 4-1

4-1 o

V4 X

CD w rH

4-1 rH

CO 0) CO

qj x

M 4-1 CO 60

60

•H

CO 3 4-J 3 •H QJ O CO CO •H 3

4-1 3

CO CO O

•H QJ CO > •H •H ^-s

CD 4-1 U CO TJ •H CO 4J

CO a- 3

rH 3 -H

r-4. cu o o < T3 o a

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1

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3

60

Pn
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o>u

3

4-1 X :::::::::::::: : •H —1 —°

r——

j

> <

— > /

> <] \

—

—

• o + *>

—

>

t> +

+ 5 *

0) •

hm 1 •

—

—

1 .

Hard —

o

eo

UJcc O Icm < *- cc

UJ

Q.

S

UJ

O H

o

o

too

T3C

CO

c

s

S-J 0)a

01

* O

CMo

CMo

I

01

5^5

C

CO

u

0)

4-1 cO

cu

s-l 60

COC

O

•H

4-1 CO>

CD Q

0)

4-J

O

"3

0)

CO CO 3

CJ 4-1 01COco

CO •H

Vj

COa

So

CJ

0) X,H

C 0) CU T3

a> o

CUu

0)a

w

TJ

V4

CO

cu

00

CN

IS00c

CO -H

CO

4-1 c

O

o

CO

01u

3

4->

CO 4J3

•HO

a

co

4-1 CO •3

CUCOo

X.

4-1

4-> a

<uu

cu

T33

cua

&

<3 H 3

COs

0)

CO

J-l c

•Hoa

co 4J

CO T3

CN

O

CN

603

733

c

CO

CU>

O

£>

CO

CO

cuu

3

4-i COu

cua

S

cu

4-1

CO a

A1ISN3Q Nl N0I1VIA3Q %

CN

CU3

00

Pn

10
4. A REVISED KLOSEK AND MCKINLEY METHOD

The Klosek and McKinley method [18] is a totally empirical recipe for

calculating the density of a LNG-like mixture given the temperature and

composition. Pressure is not taken into account. However, this does not seem to

be a serious omission. The procedure proposed by Klosek and McKinley [18] is as

follows:

V x " 2 X

i Vi - kX

CH, ( 20 ) mi* i i un«

where V . is the volume of the mixture, X. and V. are the mole fraction and mix l l

J. L. volume of the i component, X CH

is the mole fraction of methane and k is a

correction factor obtained from a table or graph. The V. and k are obviously

temperature dependent and in addition k is dependent upon the molecular weight of

the mixture.

Using the present data set k was calculated for all of the experimental data

points where methane was present in the mixture and excluding all data points

where N

2 was present in greater than 5% concentration. Figure 3 shows a typical

isotherm for k, with N~ present (labeled k~) and without N« present (labeled kj .

All of the isotherms available show similar behavior, i.e., all of the k's for

mixtures containing nitrogen (of about 5%) fall on one line and all of those for

mixtures without nitrogen fall on another. Since all of the mixtures with

nitrogen have about the same amount of nitrogen present (about 4.5%), the method

was modified by adding a term to take into account the nitrogen when it is

present. The equation becomes

V

mix E X,^ - [kj + (k2

- kj) X^/,0425] X^ (21)

where everything is the same as in eq (20) except that k, is read from one

11
E

s_

m

CO +>O

(/) •i—c

'1—>

LT> r—

r-

o

CO

+>

s-o

4-

CM

-ac

J^ IO 2 t/) CM

am X o

4-> u

w

to o

CM

If) co

r—

-(-> O

OJ

ss_oaoa

CO

s_ c

OI.X)|

12
curve and k? is read from the other. Appendix D gives tables of values for

the V., k, and k 2

which are spaced such that linear interpolation is adequate

in both variables (i.e., temperature or molecular weight). The k factors in

Appendix D have been obtained graphically from the multi component PVTx data of

Hiza and Haynes [15] and Miller and Hiza [25] as well as densities calculated

from the extended corresponding states method of section 2.

The limits of compositions of the revised Klosek and McKinley method are the

most severe of any of the methods given here. This method should not be used for

mixtures other than LNG like mixtures and for LNG like mixtures only when they

contain at least 60% methane, less than 4% nitrogen, less than 4% each of iC^H^Q

nC,H in and less than 2% total of iCrH, and nCrH, . 4 10 5 12 5 12

There are 40 experimental PVTx points from the original set of 285 which may

be considered LNG like and fall within the composition limits outlined above.

Figure 4 shows all of the deviations between calculated and experimental

densities in this 40 point comparison set which exceeds the 0.1% criterion. The

deviation trends for the revised Klosek and McKinley method (fig. 4) are very

similar to those of the hard sphere method (fig. 2) and in fact all of the

deviations in fig. 4 occur at temperatures at or above 115 K, therefore the

method can only be considered as accurate as the others for LNG like mixtures at

temperatures below 115 K.

5. THE CELL MODEL

The cell model considered here was originally proposed by Renon,

et al . [32]. In a paper by the same three authors which appeared simultaneously

(Eckert, et al . [7]), the cell model was applied to mixtures via Scott's [36]

two-fluid theory and a three parameter corresponding states theory. Albright

[2] further modified the method by modifying the mixing rules on the basis of a

13
- — <i +o •

- CO

+ «

COo

•o

>

4)

r^

%

o

sa

a

<3

u

3

4-1

O

CO

CM v£>

S

O + <

O

CM

ULJ OC

OC

LU

0.

LU

IO

CMo

o

o

CM,-

o

T3

a> 4J

CO3

o

iH

COO

C

CO

CO

4-1 s

s

•H

01a

x

<uc

<u

01&

4-) 0) £i

c

CO -C

4-» u

<u

4-1 CO

a>W)

CO3

oH

4-1 CO •H>

0) T3

3o

CO •H

J-l COa

S

oo

<u H

(UO

6

tt)

oS

3

CO ,M

<D

COO

!H

•a

0>CO •H>

a)

ai

4->

603

•H

CO3

CO

a)

5CO

6-S OvOA

4-1

A11SN3Q Nl NOI1VIA3Q %

CO3

ai

3

•H

cfl 4-1 CO T3

<U

S-J 3

4-J

•Ha

4J3

a>3

O

a.So

O

•H

4J iHi

CO •H

4-> a)CO

CO O

CN

.-I ECm

u

•H

?! +

3 3

0)a, m

a o

CNV

-a3

CO

CNJ 53

&-« <rv

•vj- V

3

v

o

j-i 3

00

•H

fa

14
proposal by Yuan [38] and by inserting a pressure dependence based on the

experimental liquid ethane data by Pope [31].

The optimization of this method was carried out by M. Albright [1] at

Phillips Petroleum Company in Bartlesville, Oklahoma and the details of this work

will be published elsewhere. The model is included here because it was optimized

to the same data set as the others and therefore the comparisons between

experimental and calculated densities given here in fig. 5 together with figs. 1,

2 and 4 provide a common basis of comparison with the other three methods. A

listing of the computer program is given in Appendix F.

The same data set as was used in the hard sphere method for comparison has

been used here, i.e., all of the data points for mixtures containing nitrogen at

temperatures 120 K and above have been taken out of the original 285 points

leaving a total of 251 data points.

As in the case of the other methods fig. 5 shows all of the points for which

the calculated and experimental densities differ by more than 0.1%.

6. USE OF THE METHODS

When the project started in 1972, the atomic weights of nitrogen, carbon and

hydrogen were taken from the 1961 carbon 12 scale, IUPAC [16]. During the course

of the investigation a revision, Atomic Weights of the Elements [3], to this

scale appeared. The revision changed slightly the atomic weights of carbon and

hydrogen, but since the changes were small (the maximum difference in any of the

densities used here is 0.003%), and because changing the atomic weights would not

change the relative results, the changes were not made. Therefore when using

the tables and programs in the appendices, the molecular weights given in the

tables and programs should be used to maintain consistency.

15
>-

35

z

UJ

a

>

m

a

1 1 © ©

1 1

0.6 _ ©

Cell Model

0.4 — —

0.2

<

+

Q

%

e

9

+

z

V

9

9

1

5 ^

+

€

+

II

V A

D

-0.2

1

1

1

1

•

O

100 110 120 130

TEMPERATURE, K

140

O mixture 2 + 11

D 12 • 13

14

15

O " 16

V 17

20

35

Q 39

© 40

9 42

€ 45 * 52

A 53

A 55

A 56

Appendix A

'igure 5. Deviations greater than 0.1% between experimental and calculated

densities using the Cell model. The comparison set is all of the data

in Appendix A except those data points for mixtures containing No at

temperatures above and including 120 K. (251 data points)

16
The critical parameters used here are from: CH», McCarty [22]; CpHg,

Sliwinski [37]; C

3 Hg, Das, et al . [4]; iC

4

H 1Q

, Das, et al . [5]; nC

4

H 1Q , Das,

et al . [6]; iC

5 H, 2

, Kudchadker, et al . [19]; and N

2

, Jacobsen, et al . [17].

Errors in the input variables will of course, cause errors in the density

predicted by the models. In general, the error in density caused by an error in

the input varibles is a function of those input variables, and must be treated on

an individual basis. However, for LNG like mixtures certain general trends are

found. An error in the pressure must be at least 50% before it will have any

effect at all on the resulting density. An error in composition, unless it is of

the order of several percent, will cause the same relative error in density as it

will cause in the molecular weight of the mixture, i.e., if an error in

composition causes a 0.1% error in the resulting molecular weight, it will also

cause a 0.1% error in the predicted density.

The error in the calculated density due to an error in the input temperature

is a function of the composition and the temperature. Table 1 gives resulting

errors in density for a 1% error in temperature, for three hypothetical LNG like

mixtures.

In general the errors in density caused by an error in temperature are the

largest for mixtures containing a high concentration of the most volatile fluids,

CH* and N«, and correspondingly the errors decrease as the concentration of

the heavier hydrocarbons increases in the mixture. These errors are not a

function of which model is being used.

When using the extended corresponding states method, one should keep in mind

that twelve significant figures are required by the methane equation of state.

The hard sphere model also uses the methane equation from McCarty [22] and the

nitrogen equation of Jacobsen, et al . [17] to calculate compressibilities and

17
TABLE 1. Errors in Density Caused by an Error in the

Input Temperature of 1%.

Temperature

K

95

100

105

110

115

Mix A = 0.95 CH

4

, 0.05 N 2

Mix B* = 0.9 CH

4

, 0.02 C

2 H

6

, 0.02 C-jHg, 0.02 iC

4

H 10 , 0.02 nC

4

H 1QJ 0.02 N

2

Mix C = 0.6 CH

4

, 0.3 C

2 Hg, 0.02 C3

Hg

, 0.02 iC

4

H 1Q , 0.02 nC

4

H 1Q , 0.02 Ng,

0.02 iC

5 H 12

.

% Error in Density

* Mix A Mix B Mix C*

0.28 0.25 0.20

0.30 0.27 0.22

0.32 0.29 0.24

0.35 0.32 0.29

0.39 0.34 0.31

Arbitrary LNG like compositions assumed for the purpose of illustrating the

effect of an error in the input temperature.

18
therefore requires twelve significant figures to insure the accuracy of the

calculated density. The other two models require only eight significant figures

to be carried along in the calculations.

7. CONCLUSIONS

On the basis of the performance of the four models given here and subject to

the composition and temperature restrictions already noted, it is estimated that

given the pressure, temperature and composition of LNG, any one of the four

models may be used to predict the density to within 0.1% of the true value. As

has already been mentioned (see section 1) the above accuracy statement is

dependent entirely upon the accuracy of the experimental data in Haynes, et al

.

[11], Haynes, et al . [13], Hiza, et al . [14], Haynes [9], Hiza and Haynes [15],

Miller and Hiza [25] and Haynes [10]. These data have been estimated by the

authors to be accurate to within 0.1% of the true value with a precision of a few

hundredths of a percent. The work on the models given here have provided no

basis for questioning the claims of the experimenters, in fact the ability of the

models to predict the densities of the multi component mixtures to within 0.1% of

the measured values tends to support the accuracy claims of the experimenters.

Interim results of this study were reported by Haynes, et al . [13] and

McCarty [23], both of which contain earlier versions of the mathematical models

given here. These earlier versions are only slightly different than the final

ones and for the purposes of calculating LNG densities either of the versions may

be used. The reader is, however, cautioned to read the limitations of each model

as defined in the earlier sections.

Computer programs for the four models are available at the Thermophysical

Properties Division of the National Bureau of Standards in Boulder, Colorado.

19
8. REFERENCES

[I] Albright, M. A., Private communication (1976).

[2] Albright, M. A., A Model for the Precise Calculation of Liquefied Natural

Gas Densities, NGPA Technical Publication TP-3 (1973).

[3] Atomic Weights of the Elements 1973, Pure and Applied Chemistry, Vol 37,

589-603 (1974).

[4] Das, T. R., Eubank, P. T., Advances in Cryogenic Engineering Vol 18,

Plenum Press, New York (1973), p. 208.

[5] Das, T. R., Eubank, P. T., Advances in Cryogenic Engineering Vol 18,

Plenum Press, New York (1973), p. 253.

[6] Das, T. R., Eubank, P. T., Advances in Cryogenic Engineering Vol 18,

Plenum Press, New York (1973), p. 244.

[7] Eckert, C. A., Renon, H. and Prausnitz, J. M. , Molecular Thermodynamics of

Simple Liquids, IEC Fund 6, 58 (1967).

[8] Goodwin, R. D., The Thermophysical Properties of Methane, from 90 to 500 K

at Pressures up to 700 Bars, Nat. Bur. Stand. (U.S.), Tech. Note 653

(1974).

[9] Haynes, W. M. , Orthobaric Liquid Densities of Methane + Isobutane and

Methane + Normal Butane Mixtures at Low Temperatures (to be published).

[10] Haynes, W. M., Measurements of Orthobaric Liquid Densities of

Multi component Mixtures of LNG Components (Np, CH», C^Hg, CoHg, iC,H,Q,

n VlO> ^5^12' n^5 H 12^ Between H° ancl 130 K, to be published.

[II] Haynes, W. M., Hiza, M. J. and Frederick, N. V., A Magnetic Suspension

Densimeter for Measurements on Fluids of Cryogenic Interest, Review of

Scientific Instruments 47, No. 10, 1237-50 (Oct 1976).

[12] Haynes, W. M. and Hiza, M. J., Measurements of the Orthobaric Liquid

Densities of Methane, Ethane, Propane, Isobutane, and Normal Butane, J.

Chem. Thermodyn., 9, 179 (1977).

20
[13] Haynes, W. M., Hiza, M. J. and McCarty, R. D., Densities of LNG for

Custody Transfer, (Proc. Fifth International Conference of LNG,

Dusseldorf, Germany), J. W. White, W. McGrew, S. Farmer, D. Hansen, H.

Jacobshagen, editors; Institute of Gas Technology, Chicago, 111., Vol. 2,

Paper II, Section III (1977).

[14] Hiza, M. J., Haynes, W. M. and Parrish, W. R., Orthobaric Liquid Densities

and Excess Volumes for Binary Mixtures of Low Molecular Weight Alkanes and

Nitrogen Between 105 and 140 K, J. Chem. Thermodyn. 9, 873 (1977).

[15] Hiza, M. J. and Haynes, W. M., Orthobaric Liquid Densities and Excess

Volumes for Multicomponent Mixtures of Low Molar Mass Alkanes and Nitrogen

Between 105 and 125 K, J. Chem. Thermodyn. JL2, 1 (1980).

[16] International Union of Pure and Applied Chemistry, 1961 Carbon 12 Scale.

[17] Jacobsen, R. T., Stewart, R. B., McCarty, R. D. and Hanley, H. J. M.,

Thermophysical Properties of Nitrogen from the Fusion Line to 3500 R

(1944 K) for Pressures to 150,000 psia (10342 x 10

5 N/m2

), Nat. Bur.

Stand. (U.S.), Technical Note No. 648 (Dec 1973).

[18] Klosek, J. and McKinley, C, Densities of Liquefied Natural Gas and of Low

Molecular Weight Hydrocarbons, Proc. First Int. Conf. on LNG, IGT, Chicago

(1968).

[19] Kudchadker, A. P., Alani, G. H. and Zwolinski, B. J., The Critical

Constants of Organic Substances, Chem. Rev. 68, 659-735 (1968).

[20] Leach, J. W. , Molecular Structure Correction for Applying the Theory of

Corresponding States to Non-Spherical Pure Fluids and Mixtures, Ph.D.

Thesis, Rice University (1967).

[21] Longuet-Higgins, H. C. and Widom, B., A Rigid Sphere Model for Melting of

Argon, Mol . Phys. 8, 549 (1964).

21
[22] McCarty, R. D., A Modified Benedict-Webb-Rubin Equation of State for

Methane Using Recent Experimental Data, Cryogenics 14, No. 5, 276-80 (May

1974).

[23] McCarty, R. D., A Comparison of Mathematical Models for the Prediction of

LN6 Densities, Nat. Bur. Stand. (U.S.), Interagency Report NBSIR 77-867

(Oct 1977).

[24] McCarty, R. D., Optimization and Comparisons of Mathematical Models for

the Prediction of Liquefied Natural Gas Densities, J. Chem. Thermodyn. (to

be published, 1980).

[25] Miller, R. C. and Hiza, M. J., Experimental Molar Volumes for Some LNG

Related Saturated Liquid Mixtures, Fluid Phase Equilibria 2, 49-57

(1978).

[26] Mollerup, J. and Rowlinson, J. S., The Prediction of Densities of

Liquefied Natural Gas and of Lower Molecular Weight Hydrocarbons, Chem.

Engng. Sci. 29 (1973).

[27] Mollerup, J., Correlated and Predicted Thermodynamic Properties of LNG and

Related Mixtures in the Normal and Critical Region, Adv. Cryog. Eng. 20,

172 (K. D. Timmerhaus, editor, Plenum Press, New York, 1975).

[28] Mollerup, J., Thermodynamic Properties of Natural Gas, Petroleum Gas, and

Related Mixtures Enthalpy Predictions, Adv. Cryog. Eng. 23, 550 (K. D.

Timmerhaus, editor, Plenum Press, New York, 1978).

[29] Orrit, J. and Olives, J. F., Density of Liquefied Natural Gas and Its

Components, Distributed at the 4th International Conference on Liquefied

Natural Gas, Algeria (1974).

[30] Orrit, J. E. and Laupretre, T. M., Density of Liquefied Natural Gas

Components, Adv. Cryog. Eng. 23, 573 (K. D. Timmerhaus, editor, Plenum

Press, New York, 1978).

22
[31] Pope, G. A., Calculation of Argon, Methane and Ethane Virial Coefficients

at Low Reduced Temperature, Ph.D. Thesis, Rice University (1971).

[32] Renon, H., Eckert, C. A. and Prausnitz, J. M., Molecular Thermodynamics of

Simple Liquids, IEC Fund. 6, 52 (1967).

[33] Rodosevich, J. B. and Miller, R. C, Calculation of LNG Excess Volumes by

a Modified Hard-Sphere Model, Adv. Cryog. Eng. 19, 339 (1974).

[34] Rodosevich, J. B., Measurements and Prediction of Liquefied Natural Gas

Densities, M.Sc. Thesis, Univ. Wyoming (1973).

[35] Rowlinson, J. S. and Watson, I. D., The Prediction of the Thermodynamic

Properties of Fluids and Fluid Mixtures - I. The Principle of

Corresponding States and Its Extensions, Chem. Engng. Sci . 2A_, 1565

(1969).

[36] Scott, R. L., J. Chem. Phys. 25, 193 (1956).

[37] Sliwinski, P. Z., Die Lorentz-Lorenz Funktion Von Dampfformigem und

Fluessiyem Athan, Propan and Butan, Phys. Chem. (Frankfurt) 63, 263

(1969).

[38] Yuan, I. C, Correlation and Prediction of Excess Properties for Selected

Binaries in the C6-C7 Hydrocarbon Boiling Range of Conformal Solution

Theory, D.Sc. Dissertation, Washington University (1971).

23
Appendix A. Experimental Data

The following is a list of all of the experimental PVTx mixtures data which

were measured during the course of this project. The data are from Miller and

Hiza [25]; Haynes and Hiza [12]; Haynes, et al . [11]; Hiza, et al . [14]; Hiza and

Haynes [15] and Haynes [9,10).

All of the data are for the orthobaric liquid except for the data of Miller

and Hiza [25] which are for the single phase liquid phase, very close to the

orthobaric conditions. The units of the data are bars, moles per liter and

kelvin. The columns labeled RKM, HS, CELL and CS correspond to percentage

derivations between experimental and predicted densities by the Revised Klosek

and McKinley, hard sphere, cell and extended corresponding states models

respectively. The derivations are always calculated using

experimental-calculated densities.

24
MIXTURE NO 1 (Miller and Hiza [25])

0.85147 CH

4 + 0.14853 C

2 Hg

P D T MW RKM HS CELL CS

.977 25.7499 110.08 18.1265 .13 - .02 .02 .01

MIXTURE NO 2 (Hiza, et al . [14])

0.68006 CH

4 + 0.31994 C

2 H6 .416 25.1027 105.00 20.5309 .14 .05 .10 .07

.645 24.7802 110.00 20.5309 .07 - .01 .02 .01

.961 24.4612 115.00 20.5309 .05 - .04 -.03 -.03

1.380 24.1402 120.00 20.5309 .06 - .06 -.06 -.05

1.930 23.8212 125.00 20.5309 .08 - .05 -.04 -.05

2.620 23.5007 130.00 20.5309 .12 - .01 .00 -.02

MIXTURE NO 3 (Hiza, et al . [14])

0.49325 CH

4

+ 0.50675 C

2

H

g .325 23.9619 105.00 23.1513 .14 .07 .11 .07 .503 23.6937 110.00 23.1513 .09 .03 .03 .03 .749 23.4328 115.00 23.1513 .11 .03 .01 .03 1.080 23.1559 120.00 23.1513 .07 - .02 -.06 -.03

1.500 22.8933 125.00 23.1513 .08 .00 -.05 .00 2.050 22.6290 130.00 23.1513 .14 .04 -.02 .03 2.720 22.3581 135.00 23.1513 .19 .06 .01 .05 3.550 22.0765 140.00 23.1513 .25 .05 .02 .04

MIXTURE NO 4 (Hiza, et al . [14])

0.35457 CH

4 + 0.64543 C2 H6 .256 23.1033 105.00 25.0965 - .04 - .07 -.04 -.07

.397 22.8777 110.00 25.0965 - .01 - .04 -.05 -.05

.580 22.6478 115.00 25.0965 .03 - .02 -.06 -.03

.826 22.4035 120.00 25.0965 .00 - .06 -.11 -.07

1.146 22.1872 125.00 25.0965 .10 .04 -.03 .03 1.550 21.9441 130.00 25.0965 .10 .03 -.04 .02

25
MIXTURE NO 5 (Hiza, et al . [14])

p

^ n4 T V.Attl

D „ u

3 ng

T MW RKM HS CELL CS

.517 24.9622 105.00 20.0279 .01 .10 .10 .07 .817 24.6332 110.00 20.0279 - .02 .08 .07 .06 1.199 24.2942 115.00 20.0279 - .04 .04 .03 .03 1.785 23.9492 120.00 20.0279 - .07 .00 .00 .00 2.415 23.5942 125.00 20.0279 - .09 - .06 -.04 -.05

3.290 23.2461 130.00 20.0279 - .11 - .06 -.01 -.04

MIXTURE NO 6 (Hiza, et a! . [14])

u . / t^cu

.478 23.4767 105.00 23.0790 .01 .02 .03 -.02

.738 23.2064 110.00 23.0790 - .03 .00 -.01 -.03

1.099 22.9364 115.00 23.0790 - .01 .00 -.02 -.02

1.582 22.6665 120.00 23.0790 .02 .01 -.01 .01 2.216 22.3818 125.00 23.0790 - .03 - .04 -.04 -.01

3.029 22.1019 130.00 23.0790 .02 - .05 -.02 .01

MIXTURE NO 7 (Hiza, et al . [14])

0.49637 CH

4 + 0.50363 C3

H8 .384 20.4909 105.00 30.1720 - .05 .01 .04 -.03

.591 20.3046 110.00 30.1720 - .08 .01 .01 -.02

.874 20.1180 115.00 30.1720 - .06 .01 -.02 -.02

1.250 19.9311 120.00 30.1720 .00 .01 -.03 .00 1.730 19.7471 125.00 30.1720 .04 .03 -.01 .04 2.320 19.5546 130.00 30.1720 - .01 .01 -.03 .05

MIXTURE NO 8 (Hiza, et al . [14])

0.29538 CH

4 + 0.70462 C3 Hg

.271 18.5132 105.00 35.8106 - .19 - .08 -.05 -.12

.409 18.3624 110.00 35.8106 - .24 - .09 -.10 -.12

26
MIXTURE NO 9 (Haynes [10])

P

on. t u.u/ £..

D

Lt MO

4

n 10 T MW RKM HS CELL CS 1.820 24.2615 120.00 19.0779 .00 .04 -.04 -.04

2.547 23 .8868 125.00 19.0779 .00 .00 -.07 -.05

3.470 23.5047 130.00 19.0779 - .01 - .03 -.09 -.07

4.616 23.1225 135.00 19.0779 .04 - .03 -.06 -.05

6.023 22.7284 140.00 19.0779 .16 - .04 -.03 -.03

MIXTURE NO 10 (Haynes [10])

0.92780 CH

4 + 0.07220 nC

4

H 10 1.270 24.6285 115.00 19.0813 .01 .08 .01 -.01

1.824 24.2783 120.00 19.0813 .07 .11 .03 .04 2.549 23.8999 125.00 19.0813 .06 .07 -.01 .01

MIXTURE NO 11 (Hiza, et al . [14])

0.91674 CH

4 + 0.08326 nC4

H 1Q

.521 25.1536 105.00 19.5467 .21 .35 .33 .22 .810 24.7960 110.00 19.5467 .12 .26 .21 .15 1.216 24.4512 115.00 19.5467 .14 .24 .18 .15 1.753 24.0889 120.00 19.5467 .10 .19 .11 .11 2.472 23.7370 125.00 19.5467 .15 .18 .10 .13 3.374 23.3789 130.00 19.5467 .17 .19 .12 .16 4.509 23.0110 135.00 19.5467 .21 .19 .15 .18 5.887 22.6391 140.00 19.5467 .35 .20 .22 .23

MIXTURE NO 12 (Haynes [10])

0.77982 CH

4 + 0.22018 nC4

H 1Q

1.702 21.6066 120.00 25.3805 .12 .14 .11 .06 2.369 21.3549 125.00 25.3805 .11 .08 .02 .04 3.228 21.1020 130.00 25.3805 .09 .00 -.07 .03 4.291 20.8555 135.00 25.3805 .12 - .03 -.10 .07 5.576 20.5978 140.00 25.3805 .20 - .13 -.15 .07

27
MIXTURE NO 13 (Haynes [10])

U ./

/

IMC

P D

nu4n

10

L T MW RKM HS CEL CS 1.179 21.8054 115.00 25.4011 .07 .15 .16 .02 1.699 21.5601 120.00 25.4011 .07 .10 .07 .02 2.372 21.3164 125.00 25.4011 .10 .06 .01 .03 3.230 21.0605 130.00 25.4011 .06 .03 -.10 .00 4.291 20.8011 135.00 25.4011 .02 .14 -.20 -.03

5.579 20.5448 140.00

MIXTURE

25.4011

NO 14 (Hiza,

.09

et al. [14])

.23 -.26 -.03

0.58828 CH

4 + 0.41172 nC4

H 1Q

3.183 18.3058 130.00 33.3687 - .32 .11 -.15 -.08

2.342 18.4853 125.00 33.3687 - .17 .00 .00 -.03

2.281 18.4772 125.00 33.3687 - .21 .05 -.04 -.08

1.636 18.6495 120.00 33.3687 - .18 .02 .07 -.06

MIXTURE NO 15 (Haynes [10])

0.92044 CH

4 + 0.07956 iC 4

H 10 1.254 24.3633 115.00 19.3910 - .21 .05 .06 -.01

1.805 24.0029 120.00 19.3910 - .24 .02 .03 -.03

2.521 23.6403 125.00 19.3910 - .22 .01 .04 -.03

3.434 23.2752 130.00 19.3910 - .21 .03 .08 .00 4.567 22.8920 135.00 19.3910 - .22 .00 .09 -.02

5.950 22.5037 140.00 19.3910 - .14 - .02 .14 -.02

MIXTURE NO 16 (Haynes [10])

0.78329 CH

4

+ 0.21671 iC

4

H 10 .782 21.9144 110.00 25.1625 - .33 .10 .15 .01 1.164 21.6652 115.00 25.1625 - .33 .05 .07 -.01

1.671 21.4136 120.00 25.1625 - .35 .01 .00 -.02

2.329 21.1668 125.00 25.1625 - .34 .00 -.03 .00 3.170 20.9125 130.00 25.1625 - .35 - .04 -.07 .00 4.208 20.6629 135.00 25.1625 - .33 - .06 -.06 .04 5.474 20.4082 140.00 25.1625 - .23 - .09 -.04 .07

28
MIXTURE NO 17 (Hiza, et al . [14])

U.HOOO/

P

on< t u.aio.

D

io .o4n

1Q T MW RKM HS CELL CS .629 17.3575 110.00 37.6362 - .62 .05 .11 .02 .938 17.2076 115.00 37.6362 - .70 .00 -.01 -.02

1.361 17.0639 120.00 37.6362 - .64 - .02 -.08 -.02

1.852 16.9156 125.00 37.6362 - .69 - .07 -.17 -.04

MIXTURE NO 18 (Hiza, et al . [14])

1.380

^ n4 T w.ut'- 26.8476

"- M

2 105.00 16.6119 - .05 - .04 -.04 -.02

1.990 26.4052 110.00 16.6119 .06 .00 .00 .04 2.634 25.9374 115.00 16.6119 .20 .01 .02 .06 3.500 25.4522 120.00 16.6119 .26 *

.03 .07 4.600 24.9496 125.00 16.6119 .54 * .04 .07 5.830 24.4210 130.00 16.6119 .69 -5 .69 .03 .05 7.300 23.8600 135.00 16.6119 .77 -3 .99 -.01 -.03

9.200 23.2809 140.00 16.6119 1.09 -2 .69 -.02 -.07

MIXTURE NO 19 (Hiza, et al . [14])

3.450 26.8735 100.00 19.6759 - .39 .06 .09 .00 4.661 26.3393 105.00 19.6759 - .56 .02 .07 .04 6.181 25.7686 110.00 19.6759 - .92 - .05 -.02 .00 8.010 25.1790 115.00 19.6759 -1.28 .13 -.08 -.03

0.112 24.5737 120.00 19.6759 -1.56 1.88 -.07 -.04

MIXTURE NO 20 (Hiza, et al . [14])

0.50758 CH

4 + 0.49242 N2 3.303 27.0801 95.00 21.9375 -2.16 .11 .14 .06 4.468 26.4588 100.00 21.9375 -1.92 - .01 .05 .04 6.383 25.8106 105.00 21.9375 -1.56 - .15 -.05 -.01

8.461 25.1387 110.00 21.9375 -1.29 - .17 -.09 -.03

10.740 24.4431 115.00 21.9375 1.12 .28 -.04 -.01

13.983 23.7096 120.00 21.9375 -1.79 3.41 .07 -.01

17.529 22.9315 125.00 21.9375 -1.14 *

.26 .00 21.076 22.1005 130.00 21.9375 - .72 -2.84 .05 .10

The hard sphere solution for the density of N2 failed.

29
MIXTURE NO 21 (Hiza, et al . [14])

0.67287 C

2 Hg + 0.32713 C

3 Hg

D r MW RKM HS CELL CS 18 .6192 125 .00 34 .6588 .00 .02 -.02 .00

18 .4648 130 .00 34 .6588 .00 .02 .00 .01 18 .3059 135 .00 34 .6588 .00 .00 .00 .00 18 .1509 140 .00 34 .6588 .00 .01 .04 .02

MIXTURE NO 22 (Hiza, et al . [14])

0.50105 C

2

H

6 + 0.49895 C 3 Hg

18.3618 105.00 37.0689 .02 .04 .02 18.2169 110.00 37.0689 .01 .00 .00

18.0726 115.00 37.0689 .00 -.03 -.01

17.9282 120.00 37.0689 - .01 -.05 -.01

17.7880 125.00 37.0689 .00 -.03 .00 17.6412 130.00 37.0689 - .02 -.04 -.02

17.4988 135.00 37.0689 - .01 -.01 -.01

17.3526 140.00 37.0689 - .03 .00 -.01

MIXTURE NO 23 (Hiza, et al . [14])

0.67117 C

2 H

g + 0.32883 nC

4

H 10 17.5047 110.00 39.2952

17.3706 115.00 39.2952

17.1031 125.00 39.2952

16.9626 130.00 39.2952

16.8285 135.00 39.2952

16.6947 140.00 39.2952

.00 .02 .00

.01 .00 .00

.02 .00 .02

.01 -.03 -.02

.00 -.01 -.01

.00 .03 .01

MIXTURE NO 24 (Hiza, et al . [14])

0.65343 C 2 Hg + 0.34657 nC4

H 10 17.2184 115.00 39.7929 .00 .00 .00 17.0824 120.00 39.7929 - .02 -.03 -.02

MIXTURE NO 25 (Hiza, et al . [14])

0.72436 C

2 Hg + 0.27564 iC

4

H 10 17.9779 105.00 37 .8030

17.8401 110.00 37.8030

17.4235 125.00 37.8030

17.2825 130.00 37.8030

.01 .01 .01

.01 .00 .01

.01 .00 .01 .00 .01 .01

30
0.68939 C

2 Hg + 0.31061 iC

4

H 1Q

MIXTURE NO 26 (Hiza, et al . [14])

D r MW RKM

17 .3716 115 .00 38 .7840

17 .2344 120 .00 38 .7840

HS CELL CS

.00 -.03 .00

.02 -.04 -.02

MIXTURE NO 27 (Hiza, et al . [14])

0.94067 C

2 Hg + 0.05933 N£ 3.850 21.4718 105.00 29.9481

4.630 21.2912 110.00 29.9481

5.472 21.0845 115.00 29.9481

6.383 20.8998 120.00 29.9481

- .02 -.01 -.03

.03 .02 .03

- .01 -.04 -.04

- .72 .01 .00

MIXTURE NO 28 (Hiza, et al . [14])

0.60949 C

3 Hg + 0.39051 nC4

H, 14.6487 115.00 49.5749 - .01 -.02 -.01

14.5521 120.00 49.5749 .02 .00 .02

MIXTURE NO 29 (Hiza, et al . [14])

0.60650 C

3 H g + 0.39350 nC

4

H 10 14.1343 140.00 49.6169

14.0333 145.00 49.6169

13.9346 150.00 49.6169

.00 -.03 .00

.00 .00 .00

.02 .05 .02

MIXTURE NO 30 (Hiza, et al . [14])

0.58692 C

3

Hg + 0.41308 nC

4

H 1Q

14.6839 110.00 49.8915

14.1748 135.00 49.8915

14.0786 140.00 49.8915

.01 .04 .01 .03 -.06 -.03

.00 -.02 .00

MIXTURE NO 31 (Hiza, et al., [14])

0.49030 C,H„np +x 0.50970 u.ju:" u iCH, '^4n io

14.3080 105.00 51.2468

14.2136 110.00 51.2468

14.1219 115.00 51.2468

14.0257 120.00 51.2468

13.9300 125.00 51.2468

13.8342 130.00 51 .2468

.01 -.04 -.01

.01 -.05 .00

.02 -.03 .02

.01 -.04 .01

.00 -.04 .00

.01 -.04 -.01

31
0.50326 C

3 Hg + 0.49674 iC4

H 1Q

MIXTURE NO 32 (Hlza, et al . [14])

D T MW RKM

13 .9718 125 .00 51 .0650

13 .8737 130 .00 51 .0650

HS CELL CS

.01 -.03 .01

- .01 -.04 -.01

MIXTURE NO 33 (Hiza, et al . [14])

0.97986 C

3 Hg + 0.02014 N2 3.567 16.2131 110.00 43.7733

4.712 16.0931 115.00 43.7733

MIXTURE NO 34 (Hi

0.96206 C

3

H g + 0.03794 N

2 4.955 16.4638 105.00 43.4870

6.708 16.3410 110.00 43.4870

- .01 -.04 -.01

- .02 -.05 -.02

[14]!

.02 -.03 .01

.00 -.04 .00

MIXTURE NO 35 (Hiza, et al . [14])

0.93260 C 3

H g + 0.06740 N

2 8.795 16.7084 105.00 43.0132 .20 .11 .18 6.313 16.8055 100.00 43.0132 .04 -.07 .01

MIXTURE NO 36 (Hiza, et al . [14])

0.52961 nC

4

H 1Q

+ 0.47039 iC

4

H 1Q

12.6943 125.00 58.1243

12.6133 130.00 58.1243

12.5271 135.00 58.1243

12.4447 140.00 58.1243

- .01 -.03 -.01

.01 -.01 .01

- .01 -.04 -.01

.00 -.02 .00

MIXTURE NO 37 (Hiza and Haynes [15])

0.80284 CH

4

+ 0.09902 CgHg + 0.09814 C

3

Hg .476 24.9975

.747 24.6696

1.119 24.3515

1.616 24.0335

105.00 20.1852 .02 .04 .06 .02

110.00 20.1852 - .03 .00 .00 -.02

115.00 20.1852 .01 .02 .02 .01 120.00 20.1852 .07 .07 .07 .06

32
MIXTURE NO 38 (Hiza and Haynes [15])

0.34242 CH

4 + 0.31372 C

2 H6 + 0. 34386 C3 Hg

P D T MW RKM HS CELL CS .427 20.5342 110.00 30.0903 - .03 .02 .00 -.03

.636 20.3497 115.00 30.0903 - .01 .03 -.02 -.02

.638 20.3567 115.00 30.0903 .03 .06 .01 .01 .914 20.1786 120.00 30.0903 .12 .10 .04 .06 .914 20.1803 120.00 30.0903 .12 .11 .05 .07 1.280 19.9858 125.00 30.0903 .10 .08 .01 .04

MIXTURE NO 39 (Hiza and Haynes [15])

0.67040 CH

4 + 0.16610 C2 Hg + 0.16350 N2 3.688 25.8587 105.00 20.3301 .57 .01 .28 .00 4.813 25.4598 110.00 20.3301 .64 - .03 .27 -.01

6.181 25.0466 115.00 20.3301 .79 .02 .25 -.05

7.731 24.6359 120.00 20.3301 .70 .42 .31 -.04

MIXTURE NO 40 (Hiza and Haynes [15])

0.34140 CH

4

+ 0.32060 C

2 Hg + 0.33800 N

2 7.190 24.9084 105.00 24.5861 2.06 .01 .61 .07 9.494 24.5350 110.00 24.5861 2.55 - .01 .64 .04

12.372 24.1433 115.00 24.5861 3.72 .24 .65 -.06

MIXTURE NO 41 (Miller and Hiza [25])

0.86786 CH

4 + 0.08181 C

3 Hg + 0.05033 iC4

H 1Q

.466 24.9239 100.00 20.4561 - .17 .04 .11 -.03

.769 24.4200 108.00 20.4561 - .17 .01 .05 -.04

1.327 23.9676 115.00 20.4561 - .18 - .01 .02 -.05

MIXTURE NO 42 (Hiza and Haynes [15])

0.79770 CH

4 + 0.10280 C-^Hg + 0.09950 N

? 2.817 25.3950 105.00 20.1181 .17 .08 .24 -.01

3.620 25.0153 110.00 20.1181 .10 .02 .23 -.05

4.549 24.6465 115.00 20.1181 .08 .08 .33 .01 5.610 24.2667 120.00 20.1181 .02 * .44 .04

The hard sphere solution for the density of N2 failed,

33
MIXTURE NO 43 (Hayne 5 [9])

0.89071 CH

4 + 0.04998 nC4

H 1Q + 0.05931 N

2

P D T MW RKM HS CELL CS 2.400 25.3450 110.00 18.8562 .23 .00 .01 .03 3.145 24.9440 115.00 18.8562 .25 - .04 -.02 .01 4.082 24.5383 120.00 18.8562 .38 * -.02 .00

5.196 24.1141 125.00 18.8562 .32 * -.04 -.04

MIXTURE NO 44 (Miller and Hiza [25])

0.85317 CH

4 + 0.05077 C2 Hg + 0.04855 C-jHg + 0.04751 nC4

H 1Q

1.038 24.6056 110.04 20.1165 .02 .15 .10 .06 1.464 24.2712 115.00 20.1165 .00 .11 .04 .02

MIXTURE NO 45 (Haynes [9])

0.85133 CH

4 + 0.05759 C2

H

6 + 0.04808 C3 Hg + 0.04300 nC

4

H 1Q

1.180 24.3243 115.00 20.0092 - .04 .07 .00 -.01

1.700 23.9965 120.00 20.0092 .00 .10 .02 .03 2.374 23.6586 125.00 20.0092 .05 .11 .04 .05 3.232 23.3108 130.00 20.0092 .04 .11 .05 .05 4.301 22.9634 135.00 20.0092 .08 .13 .11 .09

MIXTURE NO 46 (Haynes [9])

0.84566 CH

4 + 0.07924 C2 Hg + 0.05060 C3

H g + 0.02450 nC

4

H 1Q

1.167 24.5569 115.00 19.6051 .00 .04 .00 -.01

1.683 24.2126 120.00 19.6051 .02 .04 -.01 -.01

2.350 23.8698 125.00 19.6051 .08 .07 .03 .03 3.201 23.5204 130.00 19.6051 .12 .11 .09 .07

MIXTURE NO 47 (Haynes [9])

0.86040 CH

4 + 0.04600 C 2

H

6 + ° .04790 C

3 Hg + 0.04570 - C 4

H 10 1.186 24.2654 115.00 19.9552 - .14 .01 .04 -.03

1.710 23.9371 120.00 19.9552 - .10 .04 .07 .01 2.387 23.5860 125.00 19.9552 - .10 .01 .05 -.01

3.248 23.2331 130.00 19.9552 - .13 - .01 .06 -.02

4.320 22.8637 135.00 19.9552 - .18 - .07 .05 -.07

The hard sphere solution for the density of N2 failed.

34
MIXTURE NO 48 (Haynes [9])

0.85378 CH

4 + 0.05178 C2 H

6 + ° .04703 C

3 Hg + 0.04741 iC

4

H 1Q

P D T MW RKM HS CELL CS

1.190 24.2100 115.00 20.0838 - .14 .01 .04 -.03

1.706 23.8779 120.00 20.0838 - .14 .01 .04 -.02

2.379 23.5324 125.00 20.0838 - .13 - .02 .02 -.04

3.238 23.1834 130.00 20.0838 - .15 - .04 .03 -.05

MIXTURE NO 49 (Miller and Hiza [25])

0.85378 CH

4 + 0.05178 C

2

H

6 + 0.04703 C3 H8 + 0.04741 iC4

H 1Q

.972 24.5434 110.02 20.0838 - .14 .03 .06 -.01

1.429 24.2154 115.01 20.0838 - .12 .02 .05 -.01

MIXTURE NO 50 (Hiza and Haynes [15])

0.85260 CH

4 + 0.04830 C

2

H

g + 0.05070 C-jHg + 0.04840 N- 1.581 25.8910 105.00 18.7223 .01 - .04 .03 -.07

2.138 25.5081 110.00 18.7223 - .09 - .07 .03 -.07

2.827 25.1224 115.00 18.7223 - .05 - .06 .05 -.06

3.650 24.7283 120.00 18.7223 - .08 * .08 -.06

MIXTURE NO 51 (Haynes [9])

0.85892 CH

4 + 0.11532 CgHg + 0.01341 C

3 Hg + 0.00705 nC4

H 1Q + 0.00530 iC

4

H 1Q

1.185 25.0957 115.00 18.5565 .05 - .02 -.01 -.03

1.706 24.7131 120.00 18.5565 .03 - .06 -.05 -.07

2.372 24.3294 125.00 18.5565 .02 - .07 -.05 -.09

3.225 23.9490 130.00 18.5565 .05 - .02 .01 -.06

MIXTURE NO 52 (Hiza and Haynes [15])

0.85442 CH

4

+ 0.05042 C

2

H

6 + .04038 C3 Hg + 0.02901 nC4

H 10 + (). 02577 iC

4

H 1Q

.515 24.8775 105.00 20.1885 .09 .25 .25 .16 .818 24.5382 110.00 20.1885 .00 .17 .15 .09 1.190 24.2083 115.00 20.1885 .00 .15 .12 .08 1.695 23.8859 120.00 20.1885 .05 .19 .15 .13

MIXTURE NO 53 (Haynes [9])

0.84558 CH

4 + 0.08153 C

2 H6 + .04778 C

3 Hg + 0.01252 nC

4

H 10 + C1.01259 iC

4

H 1Q

1.166 24.5586 115.00 19.5838 .01 .05 .04 .01 1.680 24.2180 120.00 19.5838 .04 .07 .05 .03 2.348 23.8688 125.00 19.5838 .08 .08 .08 .04 3.188 23.5154 130.00 19.5838 .10 .10 .12 .07

The hard sphere solution for the density of N2 failed.

35
0.81249 CH

4 + 0.08484 C H

P 2.214

2.874

3.768

4.793

D 24.4562

24.1119

23.7507

23.3954

2"6

T 115.00

120.00

125.00

130.00

MIXTURE NO 54 (Haynes [9])

+ 0.04931 C

3 H g + 0.02708 nC,,H MW 20.0706

20.0706

20.0706

20.0706

RKM

.01 .00

.02

• .02

4"10

HS

.01**

-3.67

+ 0.02628 N, CELL

.03

.04 .02

.07

CS

-.02

-.01

-.05

-.03

MIXTURE NO 55 (Hiza and Haynes [15])

0.79090 CH

4 + 0.05600 C^Hg + 0.05000 C-jHg + 0.04770 nC

4

H 1Q + 0.05540 N

2 1.933 24.8080 105.00 20.9017 .04 .10 .12 .05 2.530 24.4664 110.00 20.9017 .02 .02 .03 -.02

MIXTURE NO 56 (Miller and Hiza [25])

0.79054 CH

4 + 0.05597 C

2

H

6 + 0.04996 C3 Hg + 0.04762 nC4

H 1Q + 0.05591 N

2 2.158 24.8354 105.03 20.9029 .15 .21 .23 .15

MIXTURE NO 57 (Haynes [9])

0.80940 CH

4 + 0.04542 C 2 Hg + 0.05050 C

3 Hg + 0.04667 iC4

H 10 + 0.04801 N

2 3.005 24.1487 115.00 20.6355 .02 -.02 -.03 -.04

3.863 23.8075 120.00 20.6355 - .14 * .00 -.03

4.874 23.4518 125.00 20.6355 - .12 * .01 -.05

6.125 23.0893 130.00 20.6355 - .18 -5.06 .05 -.08

MIXTURE NO 58 (Hiza and Haynes [15])

0.80600 CH

4

+ 0.04680 C

?

H

fi + 0. D4820 C

3 Hg + 0.05000 TC

4

H

1() + .04900 N

2 2.039 24.7803 105.00 20.7423 - .03 .08 .03 .01 2.550 24.4327 110.00 20.7423 - .09 - .02 -.06 -.06

3.135 24.1039 115.00 20.7423 .06 .00 -.02 -.02

3.790 23.7707 120.00 20.7423 - .10 * -.01 -.02

MIXTURE NO 59 (Miller and Hiza [25])

0.80545 CH

4

+ 0.04671 C

2 Hg + 0.04817 C-^Hg + 0.04998 iC

4

H 10 + 0.04969 N

2 2.273 24.7831 105.06 20.7476 .00 .10 .05 .03

The hard sphere solution for the density of N2 failed.

36
MIXTURE NO 60 (Haynes [9])

0.90613 CH

4 + 0.06026

+ 0.00601

C

2

H

6 +

N

2

0.02154 C

3 Hg + 0.00306 nC4

H 1Q + 0.00300 i C

4

H 10

P D T MW RKM HS CELL CS 1.478 25.3834 115.00 17.8195 .03 - .01 .01 -.01

2.043 24.9894 120.00 17.8195 .08 .00 .05 .02 2.785 24.5702 125.00 17.8195 .04 .00 .03 -.02

3.722 24.1578 130.00 17.8195 .06 -1.08 .11 .02

MIXTURE NO 61 (Haynes [9])

0.88225 CH

4 + 0.07259 C2 Hg + 0.02561 C^Hg + 0.00492 nC4

H 10

+ 0.00490 iC

4

H 10 + 0.00973 N

2 1.639 25.2023 115.00 18.3094 .09 .04 .07 .04 2.247 24.8047 120.00 18.3094 .06 .00 .04 .00

3.022 24.4022 125.00 18.3094 .04 .00 .03 -.03

MIXTURE NO 62 (Haynes [9])

0.85934 CH

4 + 0.08477

+ 0.01383

C

2

H

6 +

°

N

2

.02980 C

3 Hg + 0.00707 nC4

H 1Q + ,00519 iC

4

H 1Q

1.812 25.0384 115.00 18.7496 .12 .06 .09 .06 2.441 24.6661 120.00 18.7496 .12 *

.11 .07 3.223 24.2880 125.00 18.7496 .19 .00 .16 .09 4.222 23.8981 130.00 18.7496 .17 -2.12 .20 .10

MIXTURE NO 63 (Hiza and Haynes [15])

0.81300 CH

4 + 0.04750

+ 0.04250

C

2

H

6 +

N

2

0.04870 C

3 Hg + 0.02420 nC4

H 10 + C1.02410 iC

4

H 1Q

1.834 24.8496 105.00 20.6168 .03 .12 .10 .05 2.807 24.5159 110.00 20.6168 .02 .08 .06 .03 3.384 24.1783 115.00 20.6168 .09 .06 .05 .03 6.039 23.8577 120.00 20.6168 .04 * .11 .08

MIXTURE NO 64 (Haynes [9])

0.85341 CH

4 + 0.07898 C

2

H g + .04729 C 3 Hg + 0. 00992 nC

4

H 10 + C1.00854 iC

4

H 1Q

+ 0.00089 nC

5 H 12 + 0.00097 iC^H

12 .787 25.0063 110.00 19.3588 .01 .02 .02 -.01

1.172 24.6566 115.00 19.3588 .00 - .01 -.01 -.03

1.686 24.3079 120.00 19.3588 .02 .00 .00 -.02

2.351 23.9525 125.00 19.3588 .05 .01 .03 -.01

3.210 23.5883 130.00 19.3588 .06 .02 .06 .00

The hard sphere solution for the density of N2 failed,

37
MIXTURE NO 65 (Haynes [9])

0.75442 CH

4 + 0.15401 C2 H

6 + 0,.06950 C

3 H 8

+ .01057 nC

4

H 1Q + 0.00978 iC

4

H 1Q + 0.00083 nC

5 H 12 + 0.00089 iC,5 H 12

P D T MW RKM HS CELL CS

.723 24.2529 110.00 21.1060 - .02 .00 -.01 -.04

1.081 23.9619 115.00 21.1060 .04 .04 .03 .01 1.549 23.6535 120.00 21.1060 .07 .04 .02 .01 2.153 23.3351 125.00 21.1060 .04 .01 .00 -.01

MIXTURE NO 66 (Haynes [9])

0.75713 CH

4 + 0.13585 C

2

H

6 + 0.06742 C 3 Hg + 0.01326 nC4

H 10 + 0.01336 iC

4

H 1Q + 0.00859 N

2 + 0..00216 nC

5 H 12 + 0.00223 iC

5

H 12 1.155 24.1809 110.00 21.3094 .09 .07 .08 .04

1.595 23.8731 115.00 21.3094 .12 .05 .05 .02 2.155 23.5709 120.00 21.3094 .12 .00 .08 .05 2.873 23.2644 125.00 21.3094 .15 .00 .12 .08 3.744 22.9514 130.00 21.3094 .22 -1.42 .16 .11

MIXTURE NO 67 (Haynes [9])

0.74275 CH

4 + 0.16505 C2 H6 + 0.06547 C 3 Hg + 0.00893 nC4

H 1Q + 0.00843 iC

4

H 1Q

+ 0.00801 N2 + 0.,00067 nC

5 H 12 + 0.00069 iC

5 H 12 1.158 24.3141 110.00 21.0976 .02 - .02 .00 •.05 1.584 24.0160 115.00 21.0976 .09 .01 .02 .01

2.093 23.6937 120.00 21.0976 .03 .00 -.03 .06

2.853 23.3804 125.00 21.0976 .05 .00 -.01 .05

MIXTURE NO 68 (Haynes [9])

0.90068 CH

4 + 0.06537 C2 H

6 + 0.02200 C 3 Hg + 0.00284 nC4

H 1Q + 0.00291 iC

4

H 1Q

+ 0.00599 N

2 + 0. 00011 nC

5 H12 + 0.00010 iC

5 H 12 1.456 25.3600 115.00 17.9026 .05 .01 .03 .01 2.024 24.9656 120.00 17.9026 .08 .00 .06 .03 2.762 24.5450 125.00 17.9026 .03 .00 .03 .03 3.698 24.1289 130.00 17.9026 .02 -1.13 .07 .02

38
Appendix B. Computer Program and Equation Parameters for the

Extended Corresponding States Model

The program listings in Appendix F include the extended corresponding states

method described in section 2. To use the program in its present form one must

make one of the two possible calls to SUBROUTINE PDMIX(P,D,T,X) (lines LNG 1

through LNG 9). The two possible calls are:

CALL PDMIX(P,D,T,X)

or

CALL PMIX(P,D,T,X)

When the call to PDMIX(P,D,T,X) is made the input variables are: P (pressure in

bars); T (temperature in kelvin); and X which is a matrix of the mole fraction of

the components of the mixture in the following order:

X(l) = mole fraction of methane

X(2) = mole fraction of ethane

X(3) = mole fraction of propane

X(4) = mole fraction of normal butane

X(5) = mole fraction of isobutane

X(6) = mole fraction of nitrogen

X(7) = mole fraction of normal pentane

X(8) = mole fraction of isopentane

No other components are allowed and if one or more of the above components are

absent, a zero should be inserted in the appropriate matrix element. The program

then calculates a density and it is returned in the argument list as D (density

in moles/liter) .

When a call to PMIX(P,D,T,X) is made all of the above are the same except

that the roles of P and D are interchanged, i.e., D is an input variable and P is

calculated by the program.

39
The range of the program is 90 to 150 kelvin for the saturated liquid phase

of any of the pure components of CH, , ^0^6* ^3 H8' n^4 H 10' ^4H 10' ^2* n^4 H l2 or iC.H,^ or any mixture of those fluids. The program will extrapolate to

higher pressures (higher than saturation pressure) but the user is reminded that

such a calculation is an extrapolation and should be used with caution.

Other subprograms required:

SUBROUTINE MIX DATA, line LNG 95, Appendix F

SUBROUTINE DATA CH4, line LNG 162, Appendix F

FUNCTION FINDM, line LNG 217, Appendix F

FUNCTION SATL, line LNG 236, Appendix F

SUBROUTINE PROPS, line LNG 248, Appendix F

The equation of state from which Z and G by eqs (1) and (2) may be

derived is:

40
P = pRT + p

2

(N

1 T + N 2

T

1/2 + N 3 + N 4/T + N

5 /T

2

)

+ P 3

(N

6

T + N

y + N8 /T + N

g

/T2

)

+ P4

(N

1Q

T + N n

+ N 12/T) + P

5 (N 13 )

+ P 6

(N 14/T + N 15 /T

2

) + p

7 (N 16 /T)

+ P8

(N

1?

/T + N lg /T

2

) + p 9

(M lg/T2

)

+ P3

(N20

/T

2 + N

21

/T

3

) exp(- YP

2

) (B-l

)

+ p

5 (N 22

/T

2 + N 23

/T

4

) exp(- YP

2

)

+ P

7 (N 24

/T

2 + N 25 /T

3

) exp(- YP

2

)

+ P

9

(N 26/T

2 + N 2?

/T

4

) exp(- yp

2

)

+ P

11

(N28/T

2 + N 2g /T

3

) exp(- YP

2

)

+ p 13

(N 30 /T

2 + N

31

/T

3 + N 32 /T4

) exp(- YP

2

)

The computer subroutine PROPS(PP,DD,TT) , lines "LNG 248 through LNG 371 in

Appendix F" are the FORTRAN statements for eq (B-l) and the derivative

(aP/3p)TThe parameters for eq (B-l) as applied to methane are given in table 2 and

in the FORTRAN SUBROUTINE DATA CH4, lines LNG 162 through LNG 216, Appendix F.

The parameters for eqs (5) and (6), (9) and (10) are given in table 3 and 4

and in the FORTRAN SUBROUTINE MIX DATA (IBASE), lines LNG 95 through LNG 161,

Appendix F.

41
Table 2. Methane Coefficients Ni for Eq B-l.

R

Y

N,

N 8

0.08205616

0.0096

= -0.187027997685 x 10

0.103387108009 x 10

-1

N 3

= -0.155387625619 x 10'

N 4

= 0.772311478564 x 10

s

N

5 = -0.377103300895 x 10

s

N c = 0.846818843475 x 10

N-, = -0.496415884529

-3

0.869909352414 x 10'

N g

= -0.322821592493 x 10

N

N 10

= -0.395843026318 x 10

-4

N 110.266772318035 x 10

-1

N 12

= -0.304010057839 x 10

'13 0.191584507536 x 10

-3

N 14

= -0.195587933458 x 10

-3

'15 0.607479967879 x 10

N 16

= -0.529609525984 x 10

'17 0.152264286004 x 10

M 18

= -0.109952182842 x 10

'19

'20

0.191395549929 x 10

-3

-4

-1

-3

0.386470003746 x 10'

N 2, = -0.157930582612 x 10'

'22

'23

74

'25

'26

'27

0.195270144401 x 10*

0.165996081629 x 10'

0.603051146711

0.376485162808 x 10'

0.125593680622 x 10

-0.343570032513 x 10'

-2

N 28

= -0.540945094139 x 10

'29

'30

0.185622284663 x 10

0.770786979245 x 10

-5

-2

-8

N 31

= -0.286868318650 x

10"

*32 0.372376961647 x 10

-4

42
Table 3. Coefficients for Eqs 5 and 6.

n, = -0.109495

ru = 0.919454

n 4

= -4.14192

n r = 0.444850

n3

— -4.01525

n6

= 0.356808 n8

= 0.893323

n

7 = 1.02619 n 9

= 0.761533

*

T

c vc Flui

w (bar) (K)

3

(cm /mol

)

M No.

CH

4

0.0109 45 .956967 190.555 98 .522 16 .04303 1

C

2

H

6

0.110427 48 .60314 305.5 146 .2 30 .07012 2

C

3 H8

0.154837 42 .445123 370. 200 44 .09721 3

nC

4

H 10

0.176372 38 .295398 425. 251 .62 58 .1243 4

iC

4

H100.150115 36 .88998 408.1 263 » 58 .1243 5

N

2 0.0291791 33 .542557 126.2 89 .827 28 .0134 6

nC

5 H 12

0.234320 33 .812152 469.6 304 » 72 .15139 7

iC

5 H 12

0.288886 31 .988302 460.39 306 72 .15139 8

r Note: The large number of significant figures given for critical pressure

is necessary to reproduce the Z (Z = P V /RT ) in the least

squares fit of the data. P c

's have been converted to bar from

atmospheres.

43
00 oc

(0 en

COa-o

CO

*-> co

LO

CO

lo

4- c

O! cu O > o •r"

C7> e:o CiJ •i— t4-> <o O

<a V)

i- S- O) O)

+-> jO c E

1—

3E

>>

s- -a

fO •!- c 13 CO Li_ CO

JQ

CM

LO CM i-i O O O

O

O CDO CO

LO Csl o o o o o o

en r^ LO LO en o CM O lo CO

r—I LO en CO

I—

CM ^3- o CO o O CD CM 1—1 LO

CO en o I—

"St- LO «d- i-H o CO 1—1 r^

LO CM 1—1 en O O o en

CO lo CM

<3- i—

r»» CM LO i-H «* i—

o O O o

cm en

cm en

en lo

i-t o o

CO

LOo CM

CM CO >=* LO LO l»«. CO

CO

en

00

en

CM

en

en

en

en

CO i-H o lo

lo en

CO en

00 en

en en

en en

en en

en

en en

en o o

enen

en en

en en

en

en o o o CM en o o CO CM CD o 1—1

*d- lo CM CM CO

co en CM en r^

LO CO i—

«3- LO

en en en 00 00

co vo LO

r^ CO en I—

en 00 en «3- lo CO o lo

CO en CO r^

en en o en o CO r-. CO CM «3-

i—i CM LO CO CM LO CO r^ CO

en en en

cm co >3- lo lo r»» co

44
Table 5. Values for Checking Calculations Using Corresponding

States Equations.

0.6975 CH

4 + 0.156 C2 H6 + 0.092 C3 Hg + 0.029 nC4

H 1Q + 0.014 iC

4

H 10 + 0.0115 N

2

Temperature Density in moles/liter Pressure, bar

K

95 24.333 1 100 24.067 1.1

105 23.796 1.2

* Included for check purposes only; these values are calculated from the

corresponding states model and are not experimental data.

45
Appendix C. Computer Program and Equation Parameters for the

Hard Sphere Model

The program listing that follows is for the hard sphere model described in

section 3. To use the program in its present form one must make the following

reference to the computer program:

DEN = R0DEN(P,T,X)

where DEN is density in moles/liter, P is pressure in bars, T is temperature in

kelvin, and X is a matrix of the mole fractions of the components of the mixture

in the following order:

X(l) = mole fraction of methane

X(2) = mole fraction of ethane

X(3) = mole fraction of propane

X(4) = mole fraction of normal butane

X(5) = mole fraction of isobutane

X(6) = mole fraction of nitrogen

X(7) = mole fraction of normal pentane

X(8) = mole fraction of isopentane

Note: the inclusion of the pentanes is due to Rodosevich and Miller [33] and no

optimization of parameters has been included in this work for mixtures with

pentane as a component.

The range of the program is 90 to 150 kelvin for the saturated liquid phase

of mixtures of CH,, C^Hg, C3H g

, nC-H^Q, iC

4

H, , N2

, nCc^io anc' 1 ^5 H i?

# ^ne

program will calculate densities of any of the pure components but they will be

from a different model (i.e., some from an equation of state (CH, and N«) and

some from the equations for saturated liquid densities. Therefore in its present

form, extrapolation to higher pressures is possible but the reliability of the

results is questionable.

46
Other subprograms required:

SUBROUTINE FM, lines LNG 435 to 529, Appendix F

SUBROUTINE ZERO, lines LNG 617 to 623, Appendix F

FUNCTION FIND VI, lines LNG 530 to 548, Appendix F

FUNCTION FIND Gl, lines LNG 549 to 560, Appendix F

FUNCTION EXCESS, lines LNG 561 to 616, Appendix F

FUNCTION FIND M, lines LNG 217 to 234, Appendix F

SUBROUTINE PROPS, lines LNG 248 to 371, Appendix F

SUBROUTINE DATA CH4, lines LNG 162 to 216, Appendix F

SUBROUTINE DATA N2, lines LNG 372 to 415, Appendix F

The parameters for eq (11), section 3 are given in table 6, and in lines

LNG 462 through LNG 466 in Appendix F.

The binary interaction parameters j . . and k. . in eqs (15) and (16),

section 3 are given in table 7 and in lines LNG 447 through LNG 461 in

Appendix F.

eT'

47
Table 6. Coefficients for Eq 11.

Fluid a - S

i ci Fluid

No.

CH

4

2.755 X 10

5

3.676 x io8

1.00 1

C

2

H

6

7.773 X

5 10° 4.158 x 10"8

1.50 2

C

3

H8

14.165 X 10° 4.644 x 10"8 1.67 3

nC

4

H 1Q

22.733 X 10

5 5.051 x 10"8 1.83 4

iC

4

H

10

21.279 X

5 10° 5.056 x 10"8

1.79 5

N

2

1.718 X 10

5 3.546 x 10"8

1.03 6

nC

5

H 12

30.550 X 10

5 5.389 x 10"8

1.91 7

iC

5 H 12

42.946 X

5 10° 5.706 x IO"

8

2.11 8

b. = (2)(3.14159)(6.025 x 10

23

)S^/3

48
cr> o

*3- O

O

X o

o

o

o

o

o

cr> CM ro

>=j- i—

t

<sf CO r-« r—

CO C\J co CO i—

i

co CO 00 co

X X o .—

1

1—

1

I-- CTi Uf) O i—

•

O to

CM ID o ID O ^t- 1—

1

co

X

X

CO

r-~ 1

ro CM

i-» LT) CT> ^1-

LT) f—

1

O o

OCO

CO

CO

en

CvJ

CDO

cm ro «3- in ^d tv co

49
Appendix D. Computer Program and Parameters for the Revised

Klosek and McKinley Model

The program listing and tables that follow are for the Revised Klosek and

McKinley model described in section 4. The method may be used in two ways.

First using the equation:

V mix " £ Vl " [k

l +

< k

2

" k

l> yo.0425] fy (D-D

The V., k, and k« may be obtained from tables 8, 9 and 10 and the volume of

the mixture calculated. For example given the mixture of 0.8130 CH, + 0.0475

C

2

H

6 + 0.0487 C

3

Hg

+ 0.0242 nC

4

H 1Q + 0.0241 iC

4

H 1Q + 0.0425 N

2

and a temperature

of 105 kelvin.

The 2 X.V. and X.W. are obtained from table 8.

2xi V

i = (.8130)(. 037113) + ( .0475)( .047267) + (. 0487) ( .061766)

+ (.0242)(. 076100) + ( .0241) ( .077538) + ( .0425) ( .042565)

= 0.0409453

Then the £X.W. = ( .8130)(16. 04303) + (.0475)(30. 07012) + (.0487) (44. 09721)

+ (.0242)(58.1243) + ( .0241) (58.1243) + (.0425)(28.0143)

= 20.6168 the molecular weight of the mixture

from table 9 k, = .697 x 10"3

from table 10 k

2

= .849 x 10" 3

plugging all this into eq (D-l) gives

Vmix - .040255

1/Vmix " "mix" 24.842 moles/1 iter

This compares to the experimental value of 24.850 (Appendix A, mixture No. 63) to

within 0.03%.

50
The same result may be obtained by using the computer program in the

following way:

D = FMKM(T,X)

where T is temperature in kelvin and X is a matrix of mole fractions of the

components in the following order:

= mole fraction of methane

= mole fraction of ethane

= mole fraction of propane

= mole fraction of normal butane

= mole fraction of isobutane

= mole fraction of nitrogen

= mole fraction of normal pentane

= mole fraction of isopentane

le: T= 105., X(l) = .8130, X(2) = .0475, X(3) = .0487,

X(4) = .0242, X(5) = .0241 and X(6) = .0425.

Other subprograms required:

FUNCTION VIDEAL, lines LNG 709 through 732, Appendix F

FUNCTION SAT, lines LNG 733 through 762, Appendix F

X(D

X(2)

X(3)

X(4)

X(5)

X(6)

X(7)

X(8)

for the exampl

51
ro «3- in 00 t—

<3- CO CO 00 CO CTi in «=j- CM !—

O

O t—CO in CO

CM «3- LT> IX) r-» cn o t—CO •3- in r^. <T) r—

CO in 1-^. CTi i—

CO in r>~ CTi i—

CM <3- in CO o ro in p«» Cn I—

CO in 00 o CM *Jm CTl 1~

CO in CO

re CTi cn CTi cn o o o o O r—r—

I-H I—

CM CM CM CM CM CO CO CO T—

in CO 00 CO 00 CTi en CT> CTl CTl cn CTi cn CTi CTl CTl CTi CTi CTl CTi CTl CTi in o•r- O o o o o o o o O o O o O O o O O O O o o t—

CM

CO cn in CO o 00 in «d- CO CM CM CM CO «3" in I--O CO r*» t—

in

CM r-- r-^ 00 CTi o o H CM CO «d- in in r^- CO CTi o CM CO *3- in r^ CTi

.—i i—

CO in |-» o CM *dm 00 o CM "3-

m 00 o CO in i

CTi T—

CO CO

re CTi CTi CTi CTi o o O o o H 1—

i—

i—i—

CM CM CM CM CM CO CO r—

in CO CO oo CO CTi CTi CTi CTi CTi CTi CTl CTi CTi CTi CTi CTi cn CTl CTi CTi CTi in o o o O O O O o o O o O O O O O o O O O O .—

CM

r-.

to

+-> c

<vco

o.Eoo

CM

CO i—t o «3- r~- in r- CO CM CO t—l r—CM CTi in *i- CTl r~. in in CO

<3- 00 in in CTt 00 CM CM

Om CO CO o r— 00 i—

r^ CTi CO

m in

in o in CM CO in CO i—iO CTi o CM in i—i 00 r~^ in r>«. o in CM CO

i^-. 00 CO CTl CTi o i—

CM CO CO ID in r-^ CTi o CM <3- ID CTi t—

«3- *i- CO CO CO CO CO <3- «3- >* *d- «3- "=*• *=1- «3- ^- m in in in in m m i—i o o o O o o O O o o o o o o o o o o o o o o

CO

CM

sa*o

T3

-St «3- in CTi CO r-» CO o r-~ in in in CO o 3- CTi in CM •—I o 1—1 o 00 r-- in in in >=i- •3- «d- CO CO CO CO CO *d- •=d- ^j- in <n i*^ CO CTi

I—I o CM «3- in CO

O CM *d- in CO o CM «tfm co o CM «d- <n COO CO

rC lO in in in <n r-^ r-^ r-~ r-» 1-^ 00 00 00 CO CO CTi CTi CTi CTi CTiO «3-

«d- r^ r-^ r-~ r^ r-. r~- r-» r^ r^ r^. r-^ r^ r-^ r-» r- r-^ r^ r-^ r^ r^ 00 CM o o o o O o o o O o o o o o o o o o o o o o I—

COin

r3cr oQJ

+-> «3

SOO

CO i—i in CTi in i-H 00 in «d- >^- >^- in i^ o •* cn ^d- i-H CO r^ in o o CTl r-- in -* CO i-H o CTi co i~-~ <n in in "51- CO co CO CM CM CM

1—1 r-^ CO o CM «=dm 00 o i-H CO in r^ CTi i-H co in r^ CTi i-H CO in CO

zc <d- «* in in in in in in

m inm

m

m r- r~~ i^- i^ r-^ CO 00 CO «vt- «^- r^ r~- r-~ r^ r^ r-. i^ r-~ r-^ r*. i^ r^- r^ i^. r-^ r^ i^ i^ r~« r-^ r^ CM o o o O O o o o o o o o o o O o o o o o O t—

00

in

<D

"(- ,

i-H CM «3- i^- i-H in i-H r~- in CO CM CM «3- in CTi «=1- CTi in «d- CO CO o o m CO o r-^ in CM o r^ in CO i—

CTi l~~ in CO CM o cn co p^ <n r—1 F 00 <* in 00 cn i—i CO in in CO o CM CO in i^~ CTl 1—1 CO «* in CO o CM

V) re o o o o i-H i-H t—

1—4 i-H CM CM CM CM CM CM CO CO co CO CO •3- r-» CD </) CO m m in in m m <n in in m m m in m in in m in in m in CTi

fc= =3 o o o o o o o o o o o o o o o o o o o o o o o

«dO •I— "vtCO i—i in o r~- vt" CO CO in 00 CM CO in «d- «3- in CTi «=t i-H CTi CTi i-H oo CO CTi «3- o in CM oo «d- r—i r^- ^t- I—

00 in CM o CO in CO CM CM

QJ in o CM CO in r~- 00 o i—i co in in co o 1—1 CO in r-» CO o CM •=i- r-H r^ re in in in in in in r^ r-^ r-~ r^ r-~ r^ 00 00 00 00 co CO CTi CTi CTi o J2 CM «d- >^i- «3- ^i- •vi- «=t- *d- ^1- «=l- ^J- >vt- «* «* «3- «d- «3- «3- <3- *i- >3- "3- r^

ro 1—O

O o o O o o o o o O o o o o o o o O o o o ooCO

i—i CTi 1—

r-~ 00 ^jm CM «3- i-H in in CM <n r-~ in «*

O in o in

«* «3- in r-~ CTi CM in CTi co 00 CO CTi in CO i—

o o i-H CM in CO CO

«=i- in co o CM in r-~ CTi CM <d- r^ CTl CM in 00 i—i <d- r^ CD CO in o «3- in in in in m in in in r^ r*. r^- r^ 00 00 00 CTi CTi CT> o o o CO

rc CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO *i- <3- ^1- «3- o o o o o o o o o o o o o o o o o o o o o o o

in

i—i

s_fO *

^~ +-> 3 -C O CTi ±£ <u •i

o CM «3- in CO o CM «3- in CO o CM ^1- m 00 o CM «=S- in CO o 1— QJ

0\ CTi CTt CTi CTi CTi o O o o o i-H i-H 1—1 i—i i-H CM CM CM CM CM CO oE

jS

52
CM

LO LOO <T» 00 <T> n co cn oCM

LO

CM

OO 00 LO ro lo o o lo en

r** en

CM

CM

CM

LOCM

loen CM

lo o lo oen

CM

CM CM CM CO

CO

CM

LO o o LO LO o o o o LO

CM r-H I—1

«3- LO 00 LO •3- LO o

«d- r-« 00 en o i—1

CM «3- LO 00 I—1

CM CM

«3- CM

LO

CO LOo

CO CM LO

O LO CM en

CO LO LO CO r-» CO en

CM CM CO CO

CO

CM

OOO LO *3- CO

lo r- oo

O LO CM LO

en o o o oo CO

<—l CO

LO LO o CM .—I LO

lo r-» en CO

CM

00

en

ooo

en r--. co

LO

«3- 00o

oo oo

r--

CM CM CO CO

LO LO LO o o LO LO LO LO o en LO LO *d- LO LO o 00 LO o en CO vi- LO CM LO CO CO

O

CM LO VO r» oo en o CM CO LO CO CM LO 00 cn o CM CO 00 CM LO «* • CM • CM

CO CO .—i

r-H .—1 r—1

CM CM CO o o

t-\ LO o LO LO LO LO LO o o o CM

-* i—l en r»» CO CO «* LO .—i r^ en j*

O r—1

en I—l r~ CM CO CO CM

O .—1 LO LO LO i-» CO en O CM CO LO i-H LO r-» r-. en o CM LO en ^j- O S- CM s_ CM o i-H i—1

r—1

i—i o i-H i-H i-H i—i

CM CO

p +-> o o

<0

m

Li. u_ c O o LO LO LO o o LO o o c o CO o r~» CO CM i—i

•1— CM CO o en o o en >=d- LO CM LO CO CO

O o o «3- LO LO LO P*. CO en o CM CO T~ o LO LO LO r-» en r-1

«3- r-~ CM LO

4-> CM 4-> CM o I-H i—I

.—i o I—1

1—1

i-H CM CM

cu CO

i- sJ- s- o o

c_> o o LO LO LO o LO LO

O o o

*d- 00 CM r-» CO t—i

en en CM LO LO CO en i—i • r«- LO CO 00 CM

O

en co CO «3- ^r LO LO LO r-- en o • en CO ^t- *d- LO r-^ en CM «* en ^f" en i—t

r-H or—1

i-H 1—1 I—1

t—i

CM o

t— CD

-£> r—

its J3 \- o o o o LO o o o o LO 1—

CM LO o «3- i-~- •3- o en o CM CM 00 «3- CM en CM i-H CO LO

O

00

«—1

CM CM CO CO CO «3- LO LO r^. CO 00

r-4 CM CM CO «=j- LO r-~ en i-H «* o

LO oCM

LO

O CO LO

LO

LO

OCO oCM

CM

OLO

CM

LO LOO en «vi- o cm co «3- CM ^O «3- CM

CM CO •3" LO

CM

r-H LO CD

r-« en co

lo lo r-» r^ oo en o o o o o o o o o o o o

CO LO

LO

>3- to r~~ o o o o

*d- CM

CM CO o o

CO CO LO

«3" LO 1^. o o o O LO

en en o LO o o

LO o LO o t-H CM CM COLOCO

O LO

en en o lo o CD o .—I

53

LO CD LO

O LO

CM CM CO CO
Appendix E. Computer Program for the Cell Model

The program listings for the cell model start at line LNG 763 and continue

on to the end of Appendix F. As is mentioned in section 4, no details of the

model are given here only the program listing. To use the program in its present

form one must make the following reference to the computer program:

CALL ECKNON(P,D,T,X)

where P is input pressure in bars, D is the output density in moles/liter, T is

the input temperature in kelvins and X is a matrix of the mole fractions of the

components of the mixture in the following order:

X(l) = mole fraction of methane

X(2) = mole fraction of ethane

X(3) = mole fraction of propane

X(4) = mole fraction of normal butane

X(5) = mole fraction of isobutane

X(6) = mole fraction of nitrogen

X(7) = mole fraction of normal pentane

X(8) = mole fraction of isopentane

54
Appendix F. Computer Programs

Listing of computer programs for all four models. See the sections on the

individual models for a list of subprograms needed for each model.

The programs are written in FORTRAN IV and are operational on a CDC 6600

computer.

55
SUBROUTINE PDMIX(P,D,T,X)

C FOR A CALL TO PDMIX, P,T AND

C KELVIN AND D IS OUTPUT IN THE

C FOR A CALL TO P MIX, D,T AND

C UNITS ARE THE SAME

C THE X MATRIX MUST CONTAIN THE

C IN THE FOLLOWING 0RDER,1=C1,2

C PLACE A ZERO IN THE ELEMENTS

C PRESENT

DIMENSION ZATA(10,10),ATA(10,

1,PC(10),CF(9)

DIMENSION THETA(10,10),TH(10,

1(10,10) ,H(10, 10), HH (10, 10), VR

COMMON/DATA M/ZATA,ATA,TC ,VC,

1,PC,CF

DATA(IE=0)

D=0.0 $ PI=P/1. 01325

GO TO 4 ENTRY PMIX P=0.0

IP=1 GO TO 5 4 IP=0

5 CONTINUE

IF(IE.6T.0)G0 TO 6 IE=1

CALL DATA CH4

IBASE=L=1

CALL MIX DATA(IBASE)

6 CONTINUE

DO 1 1=1,

F(I,I)=H(I,I)=1.

THETA(I,I)=1.

1 PHI(I,I)=1.

DO 30 J=l,30

HX=FXHX=0.0

DO 10 1=1,

FH(I,I)=F(I,I)

HH(I,I)=H(I,I)

IF(X(I).LT..0001)G0 T 10

F(I,I)=(TC(I)/TC(L))*THETA(I,

H(I,I)=(VC(I)/VC(L))*PHI(I,I)

10 CONTINUE

DO 11 IA=1,N

DO 11 IB=1,N

IF(X(IA).LT..0001)G0 TO 11 IF(X( IB). LT.. 0001)60 TO 11 FAB=ZATA(IA,IB)*(F(IA,IA)* F(

HAB=ATA(IA,IB)*(.5*H(IA,IA)**

HX=HX+X(IA)*X(IB)*HAB

FXHX=FXHX+X( IA)*X( IB)*HAB*FAB

11 CONTINUE

FX=FXHX/HX

PRO=PI*HX/FX

TRO=T/FX

DEN=D*HX

IF(IP.EQ.1)G0 TO 8 DD=SATL(TR0)*1000.+1.

9 DEN=FIND M(PRO ,TRO,DD)

8 CONTINUE

IF(DEN.LE.O.O) GO TO 33 VR0=1000./DEN

DO 12 1=1,

X ARE INPUT. P IS IN BAR,T IS IN ITS OF MOLES/LITER

X ARE INPUT AND P IS OUTPUT, THE

MOL FRACTION OF THE ALLOWABLE FLUIDS

=C2,3=C3,4=NC4,5=IC4,6=N2,7=NC5,8=IC5

OF X WHERE THAT PARTICULAR GAS IS NOT

10),TC(10),VC(10),ZC(10),AC(10),W(10)

10),PHI(10,10),PH(10,10),F(10,10),FH

(10,10),TR(10,10),X(10)

W,TCO,VCO,ACO,ZCO,RR,R,OMEGO,AC,ZC,N

I)

IB, IB))**.

(l./3.)+.5*H(IB,IB)**(l./3.))**3

LNG

LNG LNG

LNG LNG

LNG

LNG

LNG 8 LNG 9 LNG 10 LNG 11 LNG 12 LNG 13 LNG 14 LNG 15 LNG 16 LNG 17 LNG 18 LNG 19 LNG 20

LNG 21 LNG 22 LNG 23

LNG 24

LNG 25 LNG 26

LNG 27 LNG 28 LNG 29 LNG 30

LNG 31 LNG 32 LNG 33 LNG 34

LNG 35 LNG 36 LNG 37 LNG 38 LNG 39 LNG 40 LNG 41 LNG 42

LNG 43

LNG 44

LNG 45 LNG 46 LNG 47 LNG 48

LNG 49 LNG 50 LNG 51 LNG 52 LNG 53 LNG 54

LNG 55 LNG 56 LNG 57 LNG 58 LNG 59

LNG 60 LNG 61 LNG 62 LNG 63

56
IF(X(I).LT..0001)G0 TO 12 VR(I,I)=VRO*PHI(I,I)/VCO

TR(I,I)=TRO*THETA(I,I)/TCO

IF(VR(I,I).GT.2.)VR(I,I)=2.

IF(VR(I,I).LT..5)VR(I,I)=.5

TH(I,I)=THETA(I,I)

THETA(I,I)=1.+(AC(I)-0MEG0)*(CF(1)-CF(2)*AL0G(TR(I,I))+(CF(3)-CF(4

1)/TR(I,I))*(VR(I,I)-CF(5)))

PH(I,I)=PHI(I,I)

PHI(I,I)=(1.+(AC(I)-0MEG0)*(CF(6)*(VR(I,I)-CF(7))-CF(8)*(VR(I,I)

1-CF(9 ) )*ALOG( TR( I , I ) ) ) )*ZCO/ZC ( I

)

12 CONTINUE

DO 13 1=1,

N

IF(X(I).LT..0001)GO TO 13 IF(ABS ((FH(I,I)-F(I,I))/F(I,I)).GT..001)GO TO 30 IF(ABS ((HH(I,I)-H(I,I))/H(I,I)).GT..001)G0 TO 30

IF(ABS ((TH(I,I)-THETA(I,I))/THETA(I,I)).GT..001)G0 TO 30

IF(ABS ((PH(I,I)-PHI(I,I))/PHI(I,I)).GT..001)G0 TO 30

13 CONTINUE

GO TO 31 30 CONTINUE

33 PRINT 100, P, DEM,

T

100 FORMAT(* ITTERATION FAILED AT*,3F10.4)

STOP

31 D=DEN/HX

THC=THETA(6,6)

IF(IP.EQ.O)GO TO 32 CALL PRESS(P,DEN,TRO)

PI=1.01325*P*FX/HX

32 RETURN

END SUBROUTINE MIX DATA(IBASE)

DIMENSION ZATA(10,10),ATA(10,10),TC(10),VC(10),ZC(10),AC(10),W(10)

1,PC(10),CF(9)

COMMON /DATA M/ZATA ,ATA ,TC , VC ,W ,TCO ,VCO ,ACO ,ZCO , RR ,R ,OMEGO , AC ,ZC ,N

1 ,PC,CF

DATA(PC=45 .356 ,47 .96757 ,41 .89008 ,37 .79462 ,36 .40758 ,33. 10393

)

DATA(TC=190.555,305.5,370.,425.,408.1,126.2)

DATA(W=16. 04303, 30. 07012, 44. 09721, 58. 1243, 58. 1243, 28. 0134)

DATA(VC=98.522,146.2,200.,251.62,263.00,89.827)

DATA(AC=. 0109,. 110427,. 154837,. 176372,. 150115,. 0291791)

DATA( R=82 .05606 ) , ( RR=8 .3144 ) , ( N=6

)

DATA(CF=-. 109495,. 919454, -4. 01525, -4. 14192,. 444850,. 356808,

11.02619, .893323, .761533)

DATA(ATA(1,2)=1. 00514), (ATA(1,3)=1. 01922), (ATA(1,4)=1. 04243),

1 (ATA(1,5)=1. 05048), (ATA(1,6)=1. 01009),

A(ATA(2,3)=1. 00599), (ATA(2,4)=1. 01616),

2( ATA(2,5)=1. 02369), (ATA( 2, 6)=1. 02127 ),(ATA( 3, 4)=1. 00172),

3(ATA(3, 5)=1. 01140) ,(ATA(3,6)=1. 04606) ,(ATA(4, 5)=. 997114),

4(ATA(4,6)=1.20955),(ATA(5,6)=1.13889)

DATA( ZATA(1, 2) =1. 01127), (ZATA( 1,3)=. 988608), (ZATA(1, 4)=. 983130),

1( ZATA( 1, 5)=. 986978), (ZATA( 1,6)=. 953430), (ZATA( 2, 3)=. 999961),

2( ZATA(2, 4)=. 972223), (ZATA(2, 5)=. 998886), (ZATA( 2, 6)=. 939622),

3(ZATA(3, 4)=. 985547) ,(ZATA(3,5)=1. 03099) ,(ZATA(3,6)=. 912209),

4(ZATA(4,5)=.976416),(ZATA(4,6)= .849200) , (ZATA( 5 ,6)=. 857310)

L=IBASE

N=8

N1=N-1

PC(7)=33.37

PC(8)=31.57

TC(7)=469.6

TC(8)=460.39

VC(7)=304.

57

LNG 64

LNG 65

LNG 66

LNG 67

LNG 68

LNG 69

LNG 70

LNG 71 LNG 72 LNG 73

LNG 74

LNG 75

LNG 76

LNG 77 LNG 78

LNG 79

LNG 80

LNG 81

LNG 82

LNG 83

LNG 84

LNG 85

LNG 86

LNG 87

LNG 88

LNG 89

LNG 90

LNG 91

LNG 92

LNG 93

LNG 94

LNG 95

LNG 96

LNG 97

LNG 98

LNG 99

LNG 100

LNG 101

LNG 102

LNG 103

LNG 104

LNG 105

LNG 106 LNG 107

LNG 108

LNG 109

LNG 110 LNG 111 LNG 112 LNG 113

LNG 114

LNG 115

LNG 116 LNG 117

LNG 118

LNG 119

LNG 120 LNG 121 LNG 122 LNG 123

LNG 124 LNG 125

LNG 126
VC(8)=306. LNG 127 W(7)=72. 15139 LNG 128

W(8)=72. 15139 LNG 129 AC (7) = .234320 LNG 130

AC (8)=. 288886 LNG 131

ATA(1,7)=ATA(1,8)=1.06 LNG 132

ATA(2,7)=ATA(2,8)=1.02 LNG 133

ATA(3,7)=ATA(3,8)=1.01 LNG 134

ATA(4,7)=ATA(4,8)=1. LNG 135

ATA(5,7)=ATA(5,8)=1. LNG 136

ATA(6,7)=ATA(6,8)=1. LNG 137

ATA(7,8)=1. LNG 138

ZATA(1,7)=ZATA(1,8)=.98 LNG 139

ZATA(2,7)=ZATA(2,8)=.99 LNG 140

ZATA(3,7)=ZATA(3,8)=.99 LNG 141 ZATA(4,7)=ZATA(4,8)=.99 LNG 142

ZATA(5,7)=ZATA(5,8)=.99 LNG 143

ZATA(6,7)=ZATA(6,8)=.99 LNG 144

ZATA(7,8)=1. LNG 145 DO 3 J=1,N1 LNG 146

J1=J+1 LNG 147 DO 3 K=J1,N LNG 148

ZATA(K,J)=ZATA(J,K) LNG 149

ATA(K,J)=ATA(J,K) LNG 150 DO 4 1=1,

LNG 151

ATA(I,I)=ZATA(I,I)=1. LNG 152

PCO=PC(L) LNG 153

VCO=VC(L) LNG 154

TCO=TC(L) LNG 155

OMEGO=AC(L) LNG 156

ZCO=PCO*VCO/TCO/R LNG 157 DO 5 1=1,

LNG 158

ZC(I)=PC(I)*VC(I)/TC(I)/R LNG 159

RETURN LNG 160 END LNG 161

SUBROUTINE DATA CH4 LNG 162

INITIALIZES THE EQUATION OF STATE CONSTANTS TO METHANE LNG 163

DIMENSION G(32),VP(9),GI(11) LNG 164

COMMON/DATA/G , R ,GAMMA , VP , DTP LNG 165

DIMENSION A(10) LNG 166

COMMON/SATC/A LNG 167 R=. 08205616 LNG 168

GAMMA=-.0096 LNG 169

A(l)=190.555 LNG 170

A(2)=10.23 LNG 171 A(3)=18. 404156472 LNG 172

A(4)=7. 3498921512 LNG 173

A(5)=-l. 4313160833 LNG 174

A(6)=A(7)=0.0 LNG 175

G( 1)=-.187027997685E-01 LNG 176

G( 2)= .103387108009E+01 LNG 177

G( 3)=-.155387625619E+02 LNG 178

G( 4)= .772311478564E+03 LNG 179

G( 5)=-.377103300895E+05 LNG 180

G( 6)= .846818843475E-03 LNG 181

G( 7)=-.496415884529E+00 LNG 182

G( 8)= .869909352414E+02 LNG 183

G( 9)=-.322821592493E+05 LNG 184

G( 10) =- .395843026318E-04 LNG 185

G(ll)= .266772318035E-01 LNG 186

G(12)=-.304010057839E+01 LNG 187

G(13)= .191584507536E-03 LNG 188

G(14)=-.195587933458E-03 LNG 189

58
10

20

G(15)= .607479967879E+01 LNG 190

G(16)=-.529609525984E-03 LNG 191

G(17)= .152264286004E-04 LNG 192

G(18)=-.109952182842E-01 LNG 193

G(19)= .191395549929E-03 LNG 194

G(20)= .386470003746E+05 LNG 195

G(21)=-.157930582612E+07 LNG 196

G(22)= .195270144401E+03 LNG 197

G(23)= .165996081629E+07 LNG 198

G(24)= .60305U46711E+00 LNG 199

G(25)= .376485162808E+02 LNG 200

G(26)= .125593680622E-02 LNG 201

G(27)=-.343570032513E+02 LNG 202

G(28)=-.540945094139E-05 LNG 203

G(29)= .185622284663E-02 LNG 204

G(30)= .770786979245E-08 LNG 205

G(31)=-.286868318650E-05 LNG 206

G(32)= .372376961647E-04 LNG 207

VP(1)=4. 77748580 LNG 208

VP(2)=1. 76065363 LNG 209

VP(3)=-. 56788894 LNG 210

VP(4)=1. 32786231 LNG 211

VP(5)=1.5 LNG 212

VP(6)=.1159 LNG 213

VP(7)=90.68 LNG 214

VP(8)=190.555 LNG 215

END LNG 216

FUNCTION FIND M(P,T,D) LNG 217

SOLVES THE EQUATION OF STATE OF METHANE FOR DENSITY GIVEN P AND T LNG 218 DD=D LNG 219

TT=T LNG 220

DO 10 1=1,50 LNG 221

CALL PRESS(PP,DD,TT) LNG 222

P2=PP LNG 223

IF(ABS (P-P2)-1.E-7*P)20,20,1 LNG 224

CALL DPDD(PP,DD,TT) LNG 225 DP=PP LNG 226

C0RR=(P2-P)/DP LNG 227

IF(ABS (C0RR)-1.E-7*DD)20,20,10 LNG 228

DD=DD-CORR LNG 229 FIND M=0 LNG 230

RETURN LNG 231 FIND M=DD LNG 232

RETURN LNG 233

END LNG 234

FUNCTION SATL(T) LNG 235

CALCULATES THE SATURATED LIQUID DENSITY OF METHANE LNG 236

DIMENSION A(10) LNG 237

COMMON /SATC/A LNG 238

IF(T.GT.A(1))G0 TO 1 LNG 239

X=(1.-T/A(D) LNG 240

SATL=A(2)+A(3)*X**(.35)+A(4)*X+A(5)*X**(4./3.)+A(6)*X**(5./3. LNG 241

)+A(7)*X**2 LNG 242

SATL=SATL/1000. LNG 243

RETURN LNG 244

SATL=1.E20 LNG 245

RETURN LNG 246 END LNG 247

SUBROUTINE PROPS(PP,DD,TT) LNG 248

EQUATION OF STATE FOR METHANE AND NITROGEN LNG 249

DIMENSION X(33) LNG 250

DIMENSION B(33),G(32) LNG 251

EQUIVALENCE (B,X) LNG 252

59
COMMON/DATA/G.R, GAMMA

DATA(ID=1)

DATA(IZ=1)

CONTINUE

D=DD

P=PP T=TT

GM=GAMMA

D2=D*D

D3=D2*D

D4=D3*D

D5=D4*D

D6=D5*D

D7=D6*D

D8=D7*D

D9=D8*D

D10=D9*D

D11=D10*D

D12=D11*D

D13=D12*D

TS=SQRT (T)

T2=T*T

T3=T2*T

T4=T3*T

T5=T4*T

F=EXP (GM*D2)

GO TO (100,200),K

ENTRY PRESS

K=l

GO TO 1 NUE =D2*T

=D2*TS

=D2

=D2/T

=D2/T2

=D3*T

=D3

=D3/T

=D3/T2

=D4*T

=D4

=D4/T

=D5

=D6/T

=D6/T2

=D7/T

=D8/T

=D8/T2

=D9/T2

=D3*F/T2

=D3*F/T3

=D5*F/T2

=D5*F/T4

=D7*F/T2

=D7*F/T3

=D9*F/T2

=D9*F/T4

=D11*F/T2

=D11*F/T3

=D13*F/T2

=D13*F/T3

=D13*F/T4

100 CONTI B ' 1) B ' 2) B 3) B [ 4) B 5) B ' 6) B 7) B 8)

Bl 9) B 10) B r ll) B '12) B r 13) B 14) B r 15) B 16) B '17) B 18) B '19) B 20) B '21) B 22) B r 23) B 24) B r 25) B 26) B r 27) B 28) B r 29) B 30) B '31) B 32)

LNG 253

LNG 254

LNG 255 LNG 256

LNG 257

LNG 258

LNG 259

LNG 260

LNG 261 LNG 262

LNG 263

LNG 264

LNG 265

LNG 266

LNG 267 LNG 268

LNG 269

LNG 270

LNG 271 LNG 272

LNG 273

LNG 274

LNG 275

LNG 276

LNG 277 LNG 278

LNG 279 LNG 280

LNG 281 LNG 282

LNG 283 LNG 284

LNG 285 LNG 286

LNG 287

LNG 288

LNG 289 LNG 290

LNG 291 LNG 292

LNG 293 LNG 294

LNG 295 LNG 296

LNG 297 LNG 298

LNG 299 LNG 300

LNG 301 LNG 302 LNG 303 LNG 304

LNG 305

LNG 306 LNG 307 LNG 308

LNG 309

LNG 310

LNG 311 LNG 312

LNG 313 LNG 314

LNG 315

60
102 P=0 LNG 316

DO 101 1=1,32 LNG 317

101 P=P+B(I)*G(I) LNG 318

P=P+R*D*T LNG 319

PP=P LNG 320

RETURN LNG 321 ENTRY DPDD LNG 322

K=2 LNG 323

60 TO 1 LNG 324

200 CONTINUE LNG 325

F1=2.00*F*GM*D LNG 326

F21=3.000*F*D2 +F1*D3 LNG 327

F22=5.000*F*D4 +F1*D5 LNG 328

F23=7.000*F*D6 +F1*D7 LNG 329

F24=9.000*F*D8 +F1*D9 LNG 330

F25=11.00*F*D10+F1*D11 LNG 331

F26=13.00*F*D12+F1*D13 LNG 332

B( 1)=2.00*D*T LNG 333

B( 2)=2.00*D*TS LNG 334

B( 3)=2.00*D LNG 335

B( 4)=2.00*D/T LNG 336

B( 5)=2.00*D/T2 LNG 337

B( 6)=3.00*D2*T LNG 338

B( 7)=3.00*D2 LNG 339

B( 8)=3.00*D2/T LNG 340

B( 9)=3.00*D2/T2 LNG 341

B(10)=4.00*D3*T LNG 342

B(11)=4.00*D3 LNG 343

B(12)=4.00*D3/T LNG 344

B(13)=5.00*D4 LNG 345

B(14)=6.00*D5/T LNG 346

B(15)=6.00*D5/T2 LNG 347

B(16)=7.00*D6/T LNG 348

B(17)=8.00*D7/T LNG 349

B(18)=8.00*D7/T2 LNG 350

B(19)=9.00*D8/T2 LNG 351

B(20)=F21/T2 LNG 352

B(21)=F21/T3 LNG 353

B(22)=F22/T2 LNG 354

B(23)=F22/T4 LNG 355

B(24)=F23/T2 LNG 356

B(25)=F23/T3 LNG 357

B(26)=F24/T2 LNG 358

B(27)=F24/T4 LNG 359

B(28)=F25/T2 LNG 360

B(29)=F25/T3 LNG 361

B(30)=F26/T2 LNG 362

B(31)=F26/T3 LNG 363

B(32)=F26/T4 LNG 364

202 P=0 LNG 365

DO 201 1=1,32 LNG 366

201 P=P+B(I)*G(I) LNG 367

P=P+R*T LNG 368 PP=P LNG 369

RETURN LNG 370 END LNG 371

SUBROUTINE DATA N2 LNG 372

INITIALIZES THE EQUATION OF STATE CONSTANTS TO NITROGEN LNG 373

DIMENSION G(32),VP(9),GI(11) LNG 374

COMMON/DATA/G,R, GAMMA, VP, DTP LNG 375

R=8.20539E-2 LNG 376

GAMMA=-.0056 LNG 377

G( 1)= 0.136224769272827E-02 LNG 378

61
G( 2)= 0.107032469908591E 00 LNG 379

G( 3)= -0.243900721871413E 01 LNG 380

G( 4)= 0.341007449376470E 02 LNG 381

G( 5)= -0.422374309466167E 04 LNG 382

G( 6)= 0.105098600246494E-03 LNG 383

G( 7)= -0.112594826522081E-01 LNG 384

G( 8)= 0.142600789270907E-03 LNG 385

G( 9)= 0.184698501609007E 05 LNG 386

G(10)= 0.811140082588776E-07 LNG 387

G(ll)= 0.233011645038006E-02 LNG 388

G(12)= -0.507752586350986E 00 LNG 389

G(13)= 0.485027881931214E-04 LNG 390

G(14)= -0.113656764115364E-02 LNG 391

G(15)= -0.707430273540575E 00 LNG 392

G(16)= 0.751706648852680E-04 LNG 393

G(17)= -0.111614119537424E-05 LNG 394

G(18)= 0.368796562233495E-03 LNG 395

G(19)= -0.201317691347729E-05 LNG 396

G(20)= -0.169717444755949E 05 LNG 397

G(21)= -0.119719240044192E 06 LNG 398

G(22)= -0.975218272038281E 02 LNG 399

G(23)= 0.554639713151823E 05 LNG 400

G(24)= -0.179920450443470E 00 LNG 401

G(25)= -0.256582926077184E 01 LNG 402

G(26)= -0.413707715090789E-03 LNG 403

G(27)= -0.256245415300293E 00 LNG 404

G(28)= -0.124222373740063E-06 LNG 405

G(29)= 0.103556535840165E-04 LNG 406

G(30)= -0.538699166558303E-09 LNG 407

G(31)= -0.757415412839596E-08 LNG 408

G(32)= 0.585367172069521E-07 LNG 409

VP(1)=5. 1113192094 $ VP(2)=6.482667539E-1 LNG 410

VP(3)=-1.5108730916E-1 $ VP(4)=7 .4028493342E-1 LNG 411

VP(5)=1.5 $ VP(6)=.123 $ VP(7)=63.15 $ VP(8)=126.26 LNG 412

VP(9)=0.0 LNG 413

DTP=31.0 LNG 414

RETURN $ END LNG 415

FUNCTION VPN(TT) LNG 416

C CALCULATES THE VAPOR PRESSURE OF BOTH METHANE AND NITROGEN LNG 417

DIMENSION G(32),VP(9) LNG 418

COMMON/DATA/G,R,GAMMA,VP,DTP LNG 419

T=TT LNG 420

X=(1.-VP(7)/T)/(1.-VP(7)/VP(8)) LNG 421

VPN=VP(6)*EXP(VP(1)*X+VP(2)*X*X+VP(3)*X**3+VP(9)*X**4+VP(4)*X* LNG 422

1(1.-X)**VP(5)) LNG 423

RETURN LNG 424

END LNG 425

FUNCTION RODEN(P,T,X) LNG 426

C THE HARD SPHERE MODEL, SEE SUBROUTINE FM FOR THE ARGUMENT LIST LNG 427

DIMENSION X(10) LNG 428

CALL FM(P,T,X,V,G) LNG 429

D=28. LNG 430

V=V+V IDEL(P,D,T,X) LNG 431

R0DEN=1000./V LNG 432

RETURN LNG 433 END LNG 434

SUBROUTINE FM(Q,T,X ,V9,G9) LNG 435

C PREDICTION OF EXCESS PROPERTIES WITH LHW POTENTIAL, COMP 1-METH LNG 436

C ANE.COMP 2-ETHANE,C0MP 3-PR0PANE,C0MP 4 N-BUTANE,COMP 5- I -BUT LNG 437

C ANE, COMP 6-NITROGEN, COMP 7-NORMAL PENTANE.COMP 8-ISOPENTANE LNG 438

C ADV CRYO ENGR. VOL. 19 (1973)-REPR0GRAMED BY R. MCCARTY, 2/22/74 LNG 439

C ARGUMENTS ARE X-MOLE FRACTIONS, T-TEMPERATURE,Q-PRESSURE,V9-EXCESS LNG 440

C VOLUME, G9-EXCESS GIBBS ENERGY, FIRST THREE ARE INPUT, LAST TWO ARE LNG 441

62
OUTPUT, INPUT IS IN KELVINS AND BAR, LNG 442

DIMENSION A(8),B(8) ,S(8) ,V(8) ,G(8) ,C(8,8) ,D(8,8) ,K(8,8)

,

LNG 443

1J(8,8),E(8),Y(8),0(8),X(10) LNG 444 TYPE REAL J,K,N1 LNG 445

DATA(KEY=1) LNG 446

DATA( J (1,2)=-. 00388616), (J( 1,3)=-. 0120932), (J( 1,4)=-. 0231577), LNG 447

A( J (1,5)=- .0238349), (J (1,6)=-. 00997547), (J (1,7)=- .0326), (J (1,8)= LNG 448

B-.0458),(J(2, 4)=-. 00400910),(J(2, 5)=-. 00812712), (J(2, 6)=-. 0143976) LNG 449

C,(J(2,7)=-.003),(J(2,8)=-.004),(J(3,4)=+.0007615710),(J(3,5)=-.003 LNG 450

D83743),(J(3,6)=-.024014),(J(3,7)=0.0),(J(3,8)=0.0),(J(4,5)=.002221 LNG 451

E50),(J(4,7)=.0),(J(4,8)=.0),(J(5,6)=-.0576043),(J(4,6)=-.0576043), LNG 452

F(J(5,7)=.0),(J(5,8)=0.0),(J(6,7)=-.04),(J(6,8)=-.05),(J(7,8)=.0) LNG 453

G ,(J(2, 3)=-. 002162) LNG 454

DATA(K( 1,2)=. 00298830), (K( 1,3)=. 0597378), (K( 1,4)=. 110893),

(

LNG 455

AK( 1,5) = . 100298), (K(l, 6) = . 0197290), (K( 1,7) = . 14), (K( 1,8) = . 1745), LNG 456

B(K(2,4)=.0677703),(K(2,5)=.0346632),(K(2,6)=.0529034),(K(2,7)= LNG 457

C.02),(K(2,8)=.03),(K(3,4)=.0249291),(K(3,5)=-.00838212),(K(4,5)=.0 LNG 458

D199213),(K(4, 6)=. 154365 ), (K(4, 7) = . 0) ,(K(4,8) = .0) ,(K(5,6) = . 154365) LNG 459

E,(K(5,7)=.0),(K(5,8)=.0),(K(6,7)=.15),(K(6,8)=.18),(K(7,8)=0.0) LNG 460

F,(K(2,3)=.014527),(K(3,6)=.14719),(K(3,7)=0.0),(K(3,8)=0.0) LNG 461

DATA(S=3.676E-8,4.158E-8,4.644E-8,5.051E-8,5.056E-8,3.546E-8, LNG 462

15.389E-8,5.706E-8) LNG 463

DATA(A=2.755E+5,7.773E+5,14.165E+5,22.733E+5,21.279E+5,1.718E+5, LNG 464

130.550E+5,42.946E+5) LNG 465

DATA(0=1., 1.5, 1.67, 1.83, 1.79, 1.03, 1.91, 2. 11) LNG 466

THESE ARE THE ACENTRICITY FACTORS (FOR MOLECULAR SHAPES, ETC.) *** LNG 467

DATA(Y=35.,45.,60.,75.,75.,40.,90.,105.) LNG 468

DATA(P1=3. 14159), (Nl=6 .025E+23) ,( R=8. 3143 ) LNG 469

IF(KEY.EQ.O)GO TO 1 LNG 470

KEY=0 LNG 471

DO 2 1=1,8 LNG 472

J(I,I)=0.0 LNG 473

K(I,I)=0.0 LNG 474

DO 2 M=I,8 LNG 475

J(M,I)=J(I,M) LNG 476

2 K(M,I)=K(I,M) LNG 477

1 CONTINUE LNG 478

P=Q*.l LNG 479

IW=8 LNG 480

DO 10 1=1, IW LNG 481

10 E(I)=0(I) LNG 482

DO 15 1=1, IW LNG 483

15 B(I)=(2./3.)*P1*N1*S(I)**3 LNG 484

DO 20 1=1, I

W

LNG 485

DO 20 M=1,IW LNG 486

D(I,M) =(((B(I)**( 1./3. ) + B(M) ** ( 1./3.))/ 2. )*(1.-J(I,M) )) LNG 487

1 **3 LNG 488

20 C( I , M ) = ( 1. - K( I, M ) ) * ( A(D* A(M) ) ** ( 1. / 2. ) * LNG 489

1( D( I, M ) **2 / ( B(I) * B(M) ) ) ** ( 1./2. ) LNG 490

A2=0 $ B2=0 LNG 491

E2=0 $ V2=0 LNG 492

DO 25 1=1, IW LNG 493

V2=V2+X(I)*Y(I) LNG 494

DO 25 M=1,IW LNG 495

E2=E2+X(I)*X(M)*(E(I)+E(M))/2. LNG 496

A2 = A2 + X(I) * X(M) * C( I, M ) LNG 497

25 B2=B2+X(I)*X(M)*D(I,M) LNG 498

V6=V2 LNG 499

DO 30 I = 1, IW LNG 500

A3 = A(I) LNG 501

B3 = B(I) LNG 502

E3 = E(I) LNG 503

V2 = Y(I) LNG 504

63
VI = FIND VI ( A3, B3, E3, R, V2, P, T) LNG 505

Gl = FIND Gl( A3, B3, E3, R, V2, P, T) LNG 506

V(I) = VI LNG 507

30 G(I) = Gl LNG 508

A3=A2 LNG 509

B3=B2 LNG 510

E3=E2 LNG 511

V2=V6 LNG 512

V1=FIND V1(A3,B3,E3,R,V2,P,T) LNG 513

C G1=FIND G1(A3,B3,E3,R,V2,P,T) LNG 514

V7=V1 LNG 515

G7=G1 LNG 516

C EXCEAS VOLUME AND GIBS ENERGY LNG 517

V9=0 LNG 518

G9=0 LNG 519

DO 35 1=1, IW LNG 520

V9=V9-X(I)*V(I) LNG 521

35 G9=G9-X(I)*G(I) LNG 522

W9 = -V9 LNG 523

H9 = -G9 LNG 524

V9=V9+V7 LNG 525

G9=G9+G7 LNG 526

VIWW=V(IWW) LNG 527

RETURN LNG 528

END LNG 529

FUNCTION FIND Vl( A3, B3, E3,R, V2, P, T ) LNG 530

C SOLVES THE HARD SPHERE EQUATION OF STATE FOR VOLUME GIVEN P AND T LNG 531

C A2 IS THE CONSTANT A, B2 IS THE CONSTANT B, E3 IS THE ACENTRICITY LNG 532 INDEX = LNG 533

1 VI = V2 LNG 534

XI = B3 / ( 4. * VI ) LNG 535

F2 = (( 1. + XI + Xl**2) / ( 1. - Xl)**3) * E3 -A3 / ( VI * R * T) LNG 536

1- (P * VI) / ( R*T) LNG 537

F3 = A3 / (R*T*V1**2) - P/ (R*T) LNG 538

F3 = F3 - ((( XI + 2.* Xl**2) * ( 1 - XI) + 3* ( 1 . + XI + <1**2 LNG 539

1* XI) / (( 1. - XI )**4 * VI)) * E3 LNG 540

V2 = VI - F2/ F3 LNG 541

IF( ABS( (V2 - VI) / V2) .LT. .00001 ) GO TO 2 LNG 542 INDEX = INDEX + 1 LNG 543

IF( INDEX .LT. 250 ) GO TO 1 LNG 544

2 VI = V2 LNG 545 FIND VI = V2 LNG 546

RETURN LNG 547 END LNG 548

FUNCTION FIND Gl( A3, B3, E3,R, V2, P, T ) LNG 549

C CALCULATES THE GIBBS FREE ENERGY FOR THE HARD SPHERE EOS LNG 550

VI = V2 LNG 551

XI = B3 / ( 4. * VI ) LNG 552

Gl =ALOG( 1. / ( 1. - XI )) +(3. *X1) / ( 1. - XI) + ( 3. * XI **2) LNG 553

1 / (2. * ( 1. - XI )**2) LNG 554

Gl = Gl - A3 / ( E3 * R * T*V1 ) + ( P * VI) / ( E3 * R * T ) -1.0 LNG 555

1 - ALOG( VI ) LNG 556

Gl = R * T * E3 * Gl LNG 557 FIND Gl = Gl LNG 558

RETURN LNG 559 END LNG 560

FUNCTION EXCESS(P,DD,T,X) LNG 561

C CALCULATES THE EXCESS OR IDEAL VOLUM DEPENDING ON THE ENTRY LNG 562

DIMENSION X(10),F(10) LNG 563

KR=0 LNG 564

GO TO 1 LNG 565 ENTRY V IDEL LNG 566

KR=1 LNG 567

64
1 CONTINUE LNG 568

CALL ZERO(F) LNG 569

IF(X(l).LE..000001)GO TO 2 LNG 570

CALL DATA CH4 LNG 571

IF(T.GT.190.555)G0 TO 12 LNG 572

PM=VPN(T)+. 00001 LNG 573

DELP=P-PM LNG 574

D=SAT(T,1) LNG 575

CALL DPDD(DP,D,T) LNG 576

DELD=DELP/DP LNG 577

D=DELD+D LNG 578

F(1)=X(1)*1000./D LNG 579

GO TO 2 LNG 580

12 D=FIND M(P,T,DD) LNG 581

IF(D.LE.0.0)D=1000. LNG 582

F(1)=X(1)*1000./D LNG 583

2 IF(X(2).LE. .OOOOODGO TO 3 LNG 584

F(2)=X(2)*1000./SAT(T,2) LNG 585

3 IF(X(3).LE.. OOOOODGO TO 4 LNG 586

F(3)=X(3)*1000./SAT(T,3) LNG 587

4 IF(X(4).LE..00001)G0 TO 5 LNG 588

F(4)=X(4)*1000./SAT(T,4) LNG 589

5 IF(X(5).LE..00001)G0 TO 6 LNG 590

F(5)=X(5)*1000./SAT(T,5) LNG 591

6 IF(X(7).LE..00001)G0 TO 61 LNG 592

F(7)=X(7)*1000./SAT(T,7) LNG 593

61 IF(X(8).LE..00001)G0 TO 62 LNG 594

F(8)=X(8)*1000./SAT(T,8) LNG 595

62 IF(X(6).LE..00001)G0 TO 8 LNG 596

CALL DATA N2 LNG 597

IF(T.GT.126.6)G0 TO 7 LNG 598

PN=VPN(T)+. 000001 LNG 599

DELP=P-PN LNG 600

D=SAT(T,6) LNG 601

CALL DPDD(DP,D,T) LNG 602

F(6)=X(6)*1000./(D+DELP/DP) LNG 603

GO TO 8 LNG 604

7 D=FIND M(P,T,DD) LNG 605

IF(D.LE.0.0)D=1000. LNG 606

F(6)=X(6)*1000./D LNG 607

8 V=1000./DD LNG 608

VS=0 LNG 609

DO 21 1=1,8 LNG 610

21 VS=VS+F(I) LNG 611

EXCESS=V-VS LNG 612

IF(KR.GT.O)EXCESS=VS LNG 613

CALL DATA CH4 LNG 614

RETURN LNG 615

END LNG 616

SUBROUTINE ZERO(X) LNG 617

INITIALIZES THE COMPONENT MATRIX TO LNG 618

DIMENSION X(10) LNG 619

DO 1 1=1,10 LNG 620

1 X(I)=0.0 LNG 621 RETURN LNG 622

END LNG 623

FUNCTION FMKM(T,X) LNG 624

THE REVISED KLOSEK AND MCKINLEY METHOD, THE INPUT IS TEMPERATURE LNG 625

AND THE COMPONENT MATRIX. TEMPERATURE IS IN KELVIN, OUTPUT IS LNG 626

DENSITY IN MOLES PER LITER. THE ALLOWABLE COMPONENTS ARE C1,C2,C3 LNG 627

NC4,IC4,N2,NC5,IC5 IN THAT ORDER. THIS METHOD SHOULD NOT BE USED LNG 628

FOR MIXTURES WITH LESS THAN 60% METHANE, OR FOR MIXTURES CONTAININ LNG 629

MORE THAN 4% NITROGEN OR MORE THAN 4% EACH OF NC4 OR IC4 OR MORE LNG 630

65
THAN 2% TOTAL OF NC5 AND IC5. DIMENSION TM(100),TN(100),X(10),Q(8)

DATA(Q= 16 .04303,30 .07012, 44 .09721, 58. 1243, 58. 1243, 28 .0134, 72. 1513

19,72.15139)

1=1, 10)=- .005,. 12,. 22,. 34,. 43,. 515,. 595,. 66,. 725,. 795)

1 = 11, 20)=-. 006,. 135,. 26,. 38,. 5,. 59,. 665,. 74,. 81,. 885)

1=21, 30)=- .007,. 15,. 3,. 425,. 575,. 675,. 755,. 83,. 91,. 99)

1=31 ,40)=-. 007,. 165,. 34,. 475,. 635,. 735,. 84,. 92, 1.045,

DATA((TM(I)

DATA((TM(I)

DATA((TM(I)

DATA((TM(I)

A1.12)

DATA((TM(I)

A, 1.245)

DATA((TM(I)

A1.38)

DATA((TM(I)

A1.55)

DATA((TM(I)

11.64,1.75)

DATA((TM(I)

Al. 86, 1.99)

DATA((TM(I)

A2. 105 ,2.272

DATA((TN(I)

DATA((TN(I)

DATA((TN(I)

DATA((TN(I)

DATA((TN(I)

11.71)

DATA((TN(I)

DATA((TN(I)

12.45)

DATA((TN(I)

1,2.9)

DATA((TN(I)

A3. 32, 3. 52)

DATA((TN(I)

1=41, 50)=- .008,. 19,. 375,. 535,. 725,. 835,. 95, 1.055, 1.155

1=51, 60)=-. 009,. 22,. 44,. 61,. 81,. 945, 1.065, 1.18, 1.28,

1=61, 70)=- .01,. 25,. 5,. 695,. 92, 1.055, 1.205, 1.33, 1.45,

1=71, 80)=-. 013,. 295,. 59,. 795, 1.035, 1.21, 1.385, 1.525,

1=81 ,90)=- .015,. 345,. 7,. 92, 1.2, 1.37, 1.555, 1.715,

1=91, 100)=-. 017,. 4,. 825, 1.06, 1.39, 1.59, 1.8, 1.95,

1=1, 10)=-. 004,. 1,. 22,. 35,. 5,. 6,. 69,. 78,. 86,. 95)

1 = 11, 20)=- .005,. 12,. 28,. 43,. 59,. 71,. 83,. 94, 1.05, 1.14)

1=21 ,30)=-. 007,. 16,. 34,. 49,. 64,. 79,. 94, 1.08, 1.17, 1.27)

1=31, 40)=- .01,. 24,. 42,. 61,. 75,. 91, 1.05, 1.19, 1.33, 1.45)

1=41, 50)=-. 015,. 32,. 59,. 77,. 92, 1.07, 1.22, 1.37, 1.52,

1=51, 60)=- .024,. 41,. 72,. 95, 1.15, 1.22, 1.3, 1.45, 1.65, 2.)

1=61, 70)=- .032,. 6,. 91, 1.23, 1.43, 1.63, 1.85, 2. 08, 2. 3,

1=71, 80)=-. 043,. 71, 1.13, 1.48, 1.73, 1.98, 2. 23, 2. 48, 2. 75

1=81, 90)=- .058,. 95, 1.46, 1.92, 2. 2, 2. 42, 2. 68, 3.,

1=91, 100)=-. 075, 1.3, 2., 2. 4, 2. 6, 3., 3. 4, 3. 77,

A3. 99, 4. 23)

IF(X(1).LT..00001)G0 TO 20

AW=0.0

DO 1 1=1,8

1 AW=AW+X(I)*Q(I)

VI=VIDEAL(T,X)

J=l

IF(T.GE.95.)J=11

IF(T.GE.100.)J=21

IF(T.GE.105.)J=31

IF(T.GE.110.)J=41

IF(T.GE.115.)J=51

IF(T.GE.120.)J=61

IF(T.GE.125.)J=71

IF(T.GE.130.)J=81

JJ=J+9

W=15.

DO 5 I=J,JJ

W=W+1

IF(AW.GT.W)GO TO 5 GO TO 6

5 CONTINUE

I=JJ

6 DIF1=AW-W

J=I-1

FK=(TM(I)-TM(J))*DIF1+TM(I)

FK1=(TM(I+10)-TM(J+10))*DIF1+TM(I+10)

IT= (T+. 00001 )/5.

66

LNG 631 LNG 632

LNG 633

LNG 634

LNG 635

LNG 636

LNG 637

LNG 638

LNG 639

LNG 640

LNG 641

LNG 642

LNG 643

LNG 644

LNG 645

LNG 646

LNG 647 LNG 648

LNG 649

LNG 650

LNG 651 LNG 652

LNG 653

LNG 654

LNG 655

LNG 656

LNG 657 LNG 658

LNG 659

LNG 660

LNG 661 LNG 662

LNG 663

LNG 664

LNG 665

LNG 666

LNG 667

LNG 668

LNG 669

LNG 670

LNG 671 LNG 672

LNG 673

LNG 674

LNG 675

LNG 676

LNG 677 LNG 678

LNG 679

LNG 680

LNG 681 LNG 682

LNG 683

LNG 684

LNG 685

LNG 686

LNG 687 LNG 688

LNG 689

LNG 690

LNG 691 LNG 692

LNG 693
DIF2=T-IT*5 LNG 694

IF(T.GE.135.)DIF2=T-130. LNG 695

IF(T.LT.90.)DIF2=T-90. LNG 696

FK=FK+(FKl-FK)*DIF2/5. LNG 697

IF(X(6).LT..0001)G0 TO 17 LNG 698

FKN=(TN(I)-TN(J))*DIF1+TN(I) LNG 699

FK1=(TN(I+10)-TN(J+10))*DIF1+TN(I+10) LNG 700

FKN=FKN+(FKl-FKN)*DIF2/5. LNG 701

FK=FK+(FKN-FK)*X(6)/.0425 LNG 702

17 FK=FK/1000. LNG 703

FMKM=1./(VI-FK*X(1)) LNG 704

RETURN LNG 705

20 FMKM=0.0 LNG 706

RETURN

V

LNG 707

END LNG 708

FUNCTION V IDEAL(T,X) LNG 709

CALCULATES THE IDEAL VOLUME OF A MIXTURE FOR THE K AND M METHOD LNG 710

DIMENSION X(10) LNG 711

V=0 LNG 712

J=0 LNG 713

IF(X(6).GT. .0001. AND. T.GT. 115. )J=1 LNG 714

DO 10 1=1,8 LNG 715

IF(X(I).LE..000001)G0 TO 10 LNG 716

IF(J.GT.0.AND.I.EQ.6)G0 TO 10 LNG 717

V=V+X(I)/SAT(T,I) LNG 718

10 CONTINUE LNG 719

IF(J.EQ.1)V=V+X(6)/SATN2(T) LNG 720

VIDEAL=V LNG 721

RETURN LNG 722 END LNG 723

FUNCTION SATN2(T) LNG 724

CALCULATES A PSEUDO SATURATED LIQUID DENSITY FOR N2 ABOVE 115 K LNG 725

IF(T.LT.115.)G0 TO 1 LNG 726

DELT=(T-115.) LNG 727

SATN2=SAT(115.,6)+DELT*(SAT(115.05,6)-SAT(114.95,6))/.l LNG 728

RETURN LNG 729

1 SATN2=SAT(T,6) LNG 730

RETURN LNG 731

END LNG 732

FUNCTION SAT(T.I) LNG 733

CALCUALTES THE PURE FLUID DENSITIES FOR THE K AND M METHOD LNG 734

UNITS ARE DEG K AND MOLES/LITER LNG 735

DIMENSION A(7,8) LNG 736

DATA((A(I) ,1=1, 7)=190. 555, 10. 16, 18. 65812322, 6. 712030737, LNG 737

1-. 9472019702, 0.0, 0.0) LNG 738

DATA((A(I),I=8,14)=305.33, LNG 739

1 6.86,12.55205121,13.43284373,-19.00461066,11.07715985,0.0) LNG 740

DATA((A(I), 1=15, 21)=369. 82, 5. ,8. 684458671, 18. 04085714, -29. 46261356 LNG 741

1,16.43559114,0.0) LNG 742

DATA((A(I),I=22,28)=425.16,3.92, LNG 743

1 7.286062567,11.96307859,-19.87591962, LNG 744

211.60211932,0.0) LNG 745

DATA((A(I),I=29,35)=408.13,3.8, LNG 746

1 7.657535400,8.145251283,-13.10582462, LNG 747

28.145894091,0.0) LNG 748

DATA((A(I), 1=36, 42)=126. 2, 11. 21, 19. 39216835, 26. 01408462, -39. 497587 LNG 749

191,23.32977312,0.0) LNG 750

DATA((A(I) , 1=43, 49)=469. 6, 3. 285, -.0362004993, 59. 00202990, LNG 751

1-93.44193819,43.66780833,0.0) LNG 752

DATA((A(I), 1=50, 56)=460. 39, 3. 271, 2. 946310456, 35. 50770979, LNG 753

1-57.41242993,28.15898339,0.0) LNG 754

IF(T.GT.A(1,I))G0 TO 1 LNG 755

X=(1.-T/A(1,D) LNG 756

67
SAT=(A(2,I)+A(3,I)*X**(.35)+A(4,I)*X+A(5,I)*X**(4./3.)

l+A(6,I)*X**(5./3.))

RETURN

1 SAT=l.E+20

RETURN

END SUBROUTINE ECKNON(PIN,DOUT,TIN,Q)

MAIN: ECKERT-RENON DENSITY MODEL

THIS PROGRAM IS DESIGNED FOR THE CALCULATION OF LNG LIQUID DENSITIES ONLY AND WILL NOT

^COMPUTE DENSITIES ABOVE 160 K.

THIS PROGRAM IS CALIBRATED SOLELY AGAINST DATA

MEASURED BY UNITED STATES DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

CRYOGENICS LABORATORY

BOULDER, COLORADO

>>>>>>>>>>>>>>NOTICE<<<<<<<<<<<<<«<<<<«<<«<<<

NO WARRANTY IS MADE OR IMPLIED AS TO THE ACCURACY

OF DENSITIES CALCULATED BY USE OF THIS MODEL.

USERS ARE AT THEIR OWN RISK IN THE USE OF THIS PROGRAM.

COMPONENT ID NUMBERS ARE

1 METHANE

2 ETHANE

3 PROPANE

4 N-BUTANE

5 I -BUTANE

6 NITROGEN

7 N-PENTANE

8 I-PENTANE

INPUT VARIABLES ARE PIN=PRESSURE IN BAR TIN=TEMPERATURE IN K Q=MATRIX OF MOLE FPRACTIONS OF COMPONENTS

OUTPUT VARIABLE IS DOUT=DENSITY IN MOLES/LITER

DIMENSION VH0LD(12),VPH0LD(12),Q(8)

TYPE INTEGER CNT1 ,CNT2, SWITCH

TYPE REAL MWM,INCR,KIJ ,MW,M0L, LAM, LAMB COMMON /RUN/ID(12),X(12),NAM(2,12),C12(12,12),R(12),Z(12),S(12),VS

1(12),TS(12),US(12),SG(12),EP(12),LAM(12),NC,MW(12),AIJ(12,12),PST(

212),TCT(12)

COMMON /DAT/TBI(12),VBI(12),TBIM(12),VBIM(12),C(12),SGIM(12),SIM(1

12),EPIM(12),PIM(12),SIN(12),VSIM(12),USIM(12),TSIM(12),DVBIM(12),P

2D(12) ,PV(12) ,RH0(12) ,VBIMP(12) ,TTM(12) ,MWM,CNT1 ,CNT2,T0LD(12) ,INCR

3(12), SWITCH ,JPC,JPCS,JMIX, DENS, VEX, HEX, GEX,TMP,VMP,TP

COMMON/PAR/KIJ( 8, 8),AJI( 8, 8)

68

LNG 757

LNG 758

LNG 759

LNG 760

LNG 761 LNG 762

LNG 763

LNG 764

LNG 765 LNG 766

LNG 767 LNG 768

LNG 769

LNG 770

LNG 771 LNG 772

LNG 773

LNG 774

LNG 775 LNG 776

LNG 777 LNG 778

LNG 779 LNG 780

LNG 781 LNG 782

LNG 783 LNG 784

LNG 785

LNG 786

LNG 787 LNG 788

LNG 789

LNG 790

LNG 791 LNG 792 LNG 793 LNG 794

LNG 795

LNG 796

LNG 797 LNG 798

LNG 799

LNG 800

LNG 801 LNG 802

LNG 803

LNG 804

LNG 805

LNG 806

LNG 807 LNG 808

LNG 809

LNG 810

LNG 811

LNG 812

LNG 813

LNG 814

LNG 815

LNG 816

LNG 817

LNG 818

LNG 819
I))

COMMON/UNITS/ITC,IPC,T,TMAX,DT,P,PMAX,DP,PS

SWITCH =

1 CALL ZER01

C THE NEXT VALUES ARE SET TO PREVENT UNDER/OVER FLOWS

TMAX = 100.0

DT = 100.0 PMAX = 100.0

DP = 100.0

PS = 100.0

CALL INPUT(Q)

CODE=0

ITC=0

IPC=0

P=PIN/1. 01325

T=TIN

IF(T.GT.(160.)) GO TO 19 8 CALL PZERO(CTMX)

MWM = DO 9 I = 1,NC

MWM = MWM + (X(I)*I*

9 CONTINUE

10 DO 11 I = 1,NC

TBI(I) = T / TS(I)

CALL VOLUME(TBI(I),VBI(I),JPUR,NC)

TBIM(I) = T / TSIM(I)

CALL V0LUME(TBIM( I) ,VBIM( I ) ,JMIX,NC)

11 CONTINUE

VM = 0.0

DO 12 I VM = VM

12 CONTINUE

TMP = ( T * 1.8) - (459.67)

DO 13 I = 1,NC

VHOLD(I) = VBI(I)

VPHOLD(I) = VBIM(I)

PP = (P*TS{I))/US(I)

VBIMP(I) = VBI(I)

CALL PRES(PP,VBIMP(I),TBI(I),NC)

VBI(I) = VBIMP(I)

PP = (P * TSIM(I)) / USIM(I)

VBIMP(I) = VBIM(I)

CALL PRES(PP,VBIMP(I),TBIM(I),NC)

VBIM(I) = VBIMP(I)

l.NC

(X(I)*VBIM(I)*VSIM(I))

13 CONTINUE

VMP = 0.0

DO 14 I = VMP = VMP PD(I) = VBIMP(I) * 14 CONTINUE

DENS=MWM/VMP

D0UT=DENS*1000./MWM

RETURN

19 DOUT=0.0

RETURN

END SUBROUTINE ZER01

COMMON /RUN/A061)

COMMON /DAT/B(224)

DO 1 I = 1,361

1 A(I) = 0.0

DO 2 I = 1,224

2 B(I) = 0.0

1,NC

+ (X(I)*VBIMP(I)*VSIM(I))

VSIM(I)

LNG 820

LNG 821

LNG 822

LNG 823

LNG 824

LNG 825

LNG 826

LNG 827

LNG 828

LNG 829

LNG 830

LNG 831

LNG 832

LNG 833

LNG 834

LNG 835

LNG 836

LNG 837

LNG 838

LNG 839

LNG 840

LNG 841

LNG 842

LNG 843

LNG 844

LNG 845

LNG 846

LNG 847

LNG 848

LNG 849

LNG 850

LNG 851

LNG 852

LNG 853

LNG 854

LNG 855

LNG 856

LNG 857

LNG 858

LNG 859

LNG 860

LNG 861

LNG 862

LNG 863

LNG 864

LNG 865

LNG 866

LNG 867

LNG 868

LNG 869

LNG 870

LNG 871

LNG 872

LNG 873

LNG 874

LNG 875

LNG 876

LNG 877

LNG 878

LNG 879

LNG 880

LNG 881

LNG 882

69
RETURN LNG 883

END LNG 884

SUBROUTINE INPUT(Q) LNG 885

DIMENSION NNO( 8) ,SIGM( 8),EPSI( 8),LAMB( 8),NAME(2, 8),SN0( 8) ,M0 LNG 886

1L( 8),CT( 8),TCH( 8),VCH( 8),ECH( 8) ,AR( 8),AZ( 8),Q(8) LNG 887 TYPE INTEGER CNT1 ,CNT2, SWITCH LNG 888 TYPE REAL MWM,INCR,KIJ,MW,MOL, LAM, LAMB LNG 889

COMMON /RUN/ID(12),X(12),NAM(2,12),C12(12,12),R(12),Z(12),S(12),VS LNG 890

1(12),TS(12),US(12),SG(12),EP{12),LAM(12),NC,MW(12),AIJ(12,12),PST( LNG 891

212),TCT(12) LNG 892

COMMON /DAT/TBI(12),VBI(12),TBIM(12),VBIM(12),C(12),SGIM(12),SIM(1 LNG 893

12),EPIM(12),PIM(12),SIN(12),VSIM(12),USIM(12),TSIM(12),DVBIM(12),P LNG 894

2D(12),PV(12),RH0(12),VBIMP(12),TTM(12),MWM,CNT1,CNT2,T0LD(12),INCR LNG 895

3(12), SWITCH ,JPC,JPCS,JMIX, DENS, VEX, HEX, GEX,TMP,VMP,TP

COMMON/PAR/KIJ( 8, 8),AJI( 8, 8)

DATA SIGM/

*0 .991000 ,1 .029000 ,1 . 155000 ,1 . 278000 , 1 .388752 ,1 .392995

,

*1. 47162, 1.47217/

DATA EPSI/

*0. 640000, 0.909000, 1.69800, 2. 237000, 2. 705262, 2. 545907,

*3. 76195, 3. 68336/

DATA LAMB/

*1. 053604, 0.986325, 1.227117, 1.408519, 1.473346, 1.461676,

*1. 698790, 1.695012/

DATA MOL/

*28. 01600, 16. 04200, 30. 06800, 44. 09400, 58. 12000, 58. 12000,

*72. 146000, 72. 146000/

DATA SNO/

*10 .00000 ,10 .00000 ,10 .00000 ,10 .00000 ,10 .00000 ,10 .00000

,

*10. 00000, 10. 00000/

DATA CT/

*126 .0600 , 190 .5600 ,305 .4300 ,369 .8200 ,425 .1600 ,408 .0300,

*469 .65,460.39/

DATA TCH/

*112. 7699, 170. 9645, 256. 8311, 294. 7255, 340. 7867, 322. 6109,

*411. 0100, 403. 3200/

DATA VCH/

*26 .01846 ,29 .04010 ,40 .88188 ,54 .60301 ,68 .72075 ,69 .44272

,

*84. 90197 ,84.99830/

DATA ECH/

*1393 .000 ,1977 .000 ,3695 .000 ,4867 .000 ,5886 .652 ,5539 .895

,

*8186. 000, 8015. 000/

DATA AR/

*1. 000000, 1.000000, 1.000000, 1.000000, 1.000000, 1.000000,

*1. 000000, 1.000000/

DATA AZ/

*10 .00000 ,10 .00000 , 10 .00000 ,10 .00000 , 10 .00000,10 .00000

,

no. ooooo, io. ooooo/

DO 4 1=2,6

4 X(I)=Q(I-1)

X(1)=Q(6)

X(7)=Q(7)

X(8)=Q(8)

NC=0

DO 1 1=1,8

IF(X(I).LE.O.O)GO TO 1 NC=NC+1

X(NC)=X(I)

ID(NC)=I

1 CONTINUE

DO 2 I = 1,NC

J = ID(I)

R(I) = AR(J)

70

LNG 896

LNG 897 LNG 898

LNG 899

LNG 900

LNG 901 LNG 902

LNG 903 LNG 904

LNG 905 LNG 906

LNG 907 LNG 908

LNG 909 LNG 910

LNG 911 LNG 912

LNG 913 LNG 914

LNG 915 LNG 916

LNG 917 LNG 918

LNG 919

LNG 920

LNG 921 LNG 922

LNG 923 LNG 924

LNG 925

LNG 926

LNG 927 LNG 928

LNG 929

LNG 930

LNG 931 LNG 932

LNG 933

LNG 934

LNG 935 LNG 936

LNG 937 LNG 938

LNG 939

LNG 940

LNG 941 LNG 942

LNG 943

LNG 944

LNG 945
Z(I) = AZ(J) LNG 946

S(I) = SNO(J) LNG 947

TS(I)= TCH(J) LNG 948

US(I)= ECH(J) LNG 949

SG(I) = SIGM(J) LNG 950

TCT(I) = CT(J) LNG 951

EP(I) = EPSI(J) LNG 952

LAM(I) = LAMB(J) LNG 953

VS(I) = VCH(J) LNG 954

MW(I) = MOL(J) LNG 955

! CONTINUE LNG 956

DO 3 I = 1,NC LNG 957

DO 3 J = 1,NC LNG 958

M = ID(I) LNG 959

L = ID(J) LNG 960

C12(I,J) = KIJ(M,L) LNG 961

C12(J,I) = KIJ(L.M) LNG 962

AIJ(I.J) = AJI(M,L) LNG 963

AIJ(J,I) = AJI(L.M) LNG 964

5 CONTINUE LNG 965

RETURN LNG 966 END LNG 967 END LNG 968

SUBROUTINE PZERO(TRT) LNG 969 TYPE INTEGER CNT1,CNT2, SWITCH LNG 970 TYPE REAL MWM, INCR,KIJ,MW,MOL, LAM, LAMB LNG 971

COMMON /RUN/ID(12),X(12),NAM(2,12),C12(12,12),R(12),Z(12),S(12),VS LNG 972

1(12),TS(12),US(12),SG(12),EP(12),LAM(12),NC,MW(12),AIJ(12,12),PST( LNG 973

212),TCT(12) LNG 974

COMMON /DAT/TBI(12),VBI(12),TBIM(12),VBIM(12),C(12),SGIM(12),SIM(1 LNG 975

12),EPIM(12),PIM(12),SIN(12),VSIM(12),USIM(12),TSIM(12),DVBIM(12),P LNG 976

2D(12),PV(12),RH0(12),VBIMP(12),TTM(12),MWM,CNT1,CNT2,T0LD(12),INCR LNG 977

3(12), SWITCH,JPC,JPCS,JMIX, DENS, VEX, HEX, GEX,TMP,VMP,TP LNG 978

COMMON/PAR/KIJ( 8, 8),AJI( 8, 8) LNG 979

COMMON /UNITS/ITC,IPC,T,TMAX,DT,P,PMAX,DP,PS LNG 980

IF(NC.EQ.l) TRT = T/TCT(1) LNG 981

IF(NC.GT.l) CALL TCM(TRT) LNG 982

IF(NC.GT.l) TRT = T/TRT LNG 983

IF(NC.EQ.l) CALL PURE(TRT,TRT,R(1) ,RXX) LNG 984

DO 1 I = 1,NC LNG 985

TCXX = T/TCTII) LNG 986

IF(NC.GT.l) CALL PURE(TCXX,TRT,R( I) ,RTR) LNG 987

JPC = LNG 988

IF(TRT.GT.(.87)) JPC = 2 LNG 989

IF(TRT.GT.d.O)) JPC = 1 LNG 990

IF(NC.EQ.l) RTR = RXX LNG 991 THERE ARE SEVERAL OTHER FORMS OF THESE EQUATIONS LNG 992 REFER TO ORIGINAL ARTICLES FOR VALUES TO USE LNG 993

S(I) = RTR * Z(I) - 2. * RTR + 2. LNG 994

SIM(I) = S(I) LNG 995

LNG 996

SGI I) = (VS(I)/RTR ) **(l./3.) LNG 997

EP(I) = US(I) / S(I) LNG 998

C(I) = LAM(I) * (2176. /((185.6)*(1. 98726))) LNG 999

TTM(I) = TS(I) LNG1000

TOLD(I) = TS(I) LNG1001

INCR(I) = (20.0) LNG1002

L CONTINUE LNG1003

JPUR = LNG1004

CNT1 = 1 LNG1005

CNT2 = 1 LNG1006

JMIX = LNG1007

I DEN = LNG1008

71
DO 3 I = 1 ,NC DEN = DEN + (X(I) * SINK I)

CONTINUE

DO 4 I = 1 ,NC

PIM(I) = (X(I) * SIM(I)) / DEN CONTINUE

DO 6 I = 1 ,NC

SGIM(I) = ( ).0 DO 6 J = 1 ,NC M = I N = J IF(I.GT.J) M = J IF(I.GT.J) N = I IF(I.EQ.J) GO TO 5 TRUDX = (AIJ(N,M)/(T/TTM(I)))

IF(TRUDX.LT. (-180.0)) GO TO 5 SGIM(I) = SGIM(I) +((PIM(J) *(((SG(I)**(l./3.) + SG(J)**(l./3.))

1/(2.0)) **3))* (AIJ(M.N) * EXP(AIJ(N,M)/(T/TTM(I)))))

GO TO 6

5 SGIM(I) = SGIM(I) +(PIM(J) *(((SG(I)**(l./3.) + SG(J)**(l./3.))

l/(2.0)))**3 ) 6 CONTINUE

DEN = 0.0

DO 7 I = l.NC

DEN = DEN + (PIM(I)* SGIM(I)* SGIM(D)

7 CONTINUE

DO 8 I = l.NC

SIN(I) =(S(I) * (SGIM(I)**(2.))) / DEN

8 CONTINUE

DO 9 I = 1,NC

TEST = (1.0) - (SIM(I) / SIN(D)

TEST = ABS (TEST)

IF(TEST.GT. (0.00001) ) GO TO 10

9 CONTINUE

GO TO 12 10 DO 11 I = 1,NC

SIM(I) =(SIM(I) + SIN(D) /(2.0)

11 CONTINUE

CNT1 = CNT1 + 1 IF(CNT1.GT.250) GO TO 12 GO TO 2 12 DO 14 I = 1,NC

SIM(I) = SIN(I)

EPIM(I) = 0.0

DO 14 J = 1,NC

K = I L = J IF(J.LT.I) K = J IF(J.LT.I) L = I IF(I.EQ.J) GO TO 13 TRUDX = C12(L,K) / (T/TTM(I))

IF(TRUDX.LT. (-180.0)) GO TO 13 EPIM(I) = EPIM(I) +((PIM(J) * SQRT(EP(I)*EP(J)))*

1(C12(K,L) * EXP((C12(L,K) /(T/TTM( I) ) )) )) GO TO 14

13 EPIM(I) = EPIM(I) + (PIM(J) * SQRT(EP(I) * EP(J)))

14 CONTINUE

ASSUME NUMBER OF MOLS OF MIXTURE = 1.0 DO 15 I = l.NC

VSIM(I) = R(I) * (SGIM(I)**(3.0))

USIM(I) = SIM(I) * EPIM(I)

TSIM(I) = USIM(I) / ((1.98726) * C(D)

72

LNG1009

LNG1010

LNG1011

LNG1012

LNG1013

LNG1014

LNG1015

LNG1016

LNG1017

LNG1018

LNG1019

LNG1020

LNG1021

LNG1022

LNG1023

LNG1024

LNG1025

LNG1026

LNG1027

LNG1028

LNG1029

LNG1030

LNG1031

LNG1032

LNG1033

LNG1034

LNG1035

LNG1036

LNG1037

LNG1038

LNG1039

LNG1040

LNG1041

LNG1042

LNG1043

LNG1044

LNG1045

LNG1046

LNG1047

LNG1048

LNG1049

LNG1050

LNG1051

LNG1052

LNG1053

LNG1054

LNG1055

LNG1056

LNG1057

LNG1058

LNG1059

LNG1060

LNG1061

LNG1062

LNG1063

LNG1064

LNG1065

LNG1066

LNG1067

LNG1068

LNG1069

LNG1070

LNG1071
15 CONTINUE

DO 16 I = 1,NC

TEST = (1.0) - (TSIM(I)/TTM(I))

TEST = ABS(TEST)

IF(TEST.GT. (0.00001)) GO TO 17 16 CONTINUE

RETURN

17 DO 20 I = 1,NC

IF(TSIMU) - TTM(I))18,20,19

18 TNEW = TTM(I) - INCR(I)

IF(TNEW.EQ.TOLD(I)) INCR(I) = INCR(I)/ (2.0)

IF(TNEW.EQ.TOLDU)) GO TO 18

TOLD(I) = TTM(I)

TTM(I) = TNEW

GO TO 20

19 TNEW = TTM(I) + INCR(I)

IF(TNEW.EQ.TOLDd)) INCR(I) = INCR(I) / (2.0)

IF(TNEW.EQ.TOLDd)) GO TO 19 TOLD(I) = TTM(I)

TTM(I) = TNEW

20 CONTINUE

CNT2 = CNT2 + 1 IF(CNT2.GT.250) RETURN

GO TO 2 END SUBROUTINE PURE(TZ,T,Z,R)

DIMENSION A(15)

IF(TZ.LT.(. 8653525)) R = Z IF(TZ.LT.(. 8653525)) GO TO 2 IF(T.LT.(. 8653525)) R = Z IF(T.LT.(. 8653525)) GO TO 2 IF(T.GT.d.O)) TA = 1.0

IF(T.LE.d.O)) TA = T DATA A/ .9184780 ,- .1530647 ,- .1090050 , .8073883 ,1 .441803

,

1-10. 85944, -6. 041687, 51. 26758,. 9062500, -108. 9805, 28. 88672,

2106 . 1406 ,-45 .78125 ,-38 .43750 ,20 .56250/

R = 0.0

TT = (TA - (.9267292)) / ( .7267517E-01)

DO 1 K = 1,14

R = R + A(16-K)

R = R * TT

1 CONTINUE

R = R + A(l)

2 RETURN

END SUBROUTINE VOLUME(T,V ,J ,NC) TR = T IF(TR.GT.d.OO)) GO TO 4

V = 0.5

1 VT = (1.0) + (0.1*TR*V**(4.0))

ERR = (1.0) - (V/VT)

TEST = ABS(ERR)

IF(TEST.LE. (0.00001)) GO TO 2 V = VT

GO TO 1 2 V = V**(3.0)

3 RETURN

4 V = ((((((10.06600 *TR)-24.79837)*TR)+23.260722)*TR)-6. 686880)

GO TO 3 END SUBROUTINE BETA(P,DV,T,V,KK)

73

LNG1072

LNG1073

LNG1074

LNG1075

LNG1076

LNG1077

LNG1078

LNG1079

LNG1080

LNG1081

LNG1082

LNG1083

LNG1084

LNG1085

LNG1086

LNG1087

LNG1088

LNG1089

LNG1090

LNG1091

LNG1092

LNG1093

LNG1094

LNG1095

LNG1096

LNG1097

LNG1098

LNG1099

LNG1100

LNG1101

LNG1102

LNG1103

LNG1104

LNG1105

LNG1106

LNG1107

LNG1108

LNG1109

LNG1110

LNG1111

LNG1112

LNG1113

LNG1114

LNG1115

LNG1116

LNG1117

LNG1118

LNG1119

LNG1120

LNG1121

LNG1122

LNG1123

LNG1124

LNG1125

LNG1126

LNG1127

LNG1128

LNG1129

LNG1130

LNG1131

LNG1132

LNG1133

LNG1134
TYPE REAL AF,BF,CF,DF,EF,AG,BG,CG,DG,P,DV,T,V,F,F1 ,G,G1 , DEN, EG LNG1135

TYPE REAL C,B1,B2,B3 LNG1136

DIMENSION C(ll) LNG1137

DATA AF/0.11566564E+02/,BF/-0.53510144E+01/,CF/-0.74598207E-01/, LNG1138

lDF/0.67068653E+00/,EF/-0.11939887E+00/,AG/0.62721813E+01/, LNG1139

2BG/0 .47698365E+00/ ,CG/-0 .16023080E+01/ ,DG/0 .49837746E+00/

,

LNG1140

3EG/-0.42639183E-01/ LNG1141

F = AF +(BF*V)+(CF*V*V)+ (DF*V*V*V)+(EF*V*V*V*V) LNG1142

IF(F.LT.(0.0)) GO TO 1 LNG1143

Fl = (BF+(CF*V*2.E+00)+(DF*V*V*3.E+00)+(EF*V*V*V*4.E+00))* LNG1144

IT * EXP(F) LNG1145

G = AG+(BG*V)+(CG*V*V)+(DG*V*V*V)+(EG*V*V*V*V) LNG1146

IF(G.LT.(0.00)) GO TO 1 LNG1147

Gl = (BG+(CG*V*2.E+00)+(DG*V*V*3.E+00+(EG*V*V*V*4.E+00))) * EXP(G LNG1148

1) LNG1149

Gl = -Gl LNG1150

DEN = Fl + Gl LNG1151

DV = (l.E+OO) / DEN LNG1152

IF(DV.GT.(0.0).OR.DV.LT.(-1.0E+00)) GO TO 1 . LNG1153

GO TO 2 LNG1154

DATA C/-.118659822E+02,-.5509099E+00,.4172102E+01,-.8996686E+00, LNG1155

1- .1500376E+01 ,- .1958324E+00,- .2788988E+01 , .5195283E+00, LNG1156

2.3734878E+01,.1361904E+00,.4671948E-01/ LNG1157

1 Bl = C(l) + C(2)*T + C(3)*V LNG1158

B2 = C(4)*((V+C(5))**(2 ))*EXP((C(6))*((T+C(7))**(2 ))) LNG1159

B3 = C(ll) * (V+C(8))**(C(9))/(T**(C(10))) LNG1160

DV = Bl + B2 + B3 LNG1161

DV = EXP(DV) LNG1162

DV = - DV LNG1163

2 RETURN LNG1164

END LNG1165

SUBROUTINE PRES(A,B,C,NC) LNG1166

TYPE REAL H,P,V,T,K1,K2,K3,K4,VT,PT LNG1167

P = A LNG1168

V = B LNG1169

T = C LNG1170

H = l.E-02 LNG1171

IF(H.GT.P) H = P LNG1172

ASSIGN 3 TO KK LNG1173

1 CALL BETA(P,K1,T,V,NC) LNG1174

Kl = H * Kl LNG1175

VT = V + ((0.5E+00) *K1) LNG1176

PT = P + ((0.5E+00)*H) LNG1177

CALL BETA(PT,K2,T,VT,NC) LNG1178

K2 = K2 * H LNG1179

VT = V + ((0.5E+00) *K2) LNG1180

CALL BETA(PT,K3,T,VT,NC) LNG1181

K3 = K3 * H LNG1182

PT = P + H LNG1183

VT = V + ( K3) LNG1184

CALL BETA(PT,K4,T,VT,NC) LNG1185

K4 = K4 * H LNG1186

V = V + (((Kl + (2.E+00*K2) + (2.E+00*K3) + K4) / (6.E+00)) ) LNG1187

P = P - H LNG1188

IF(P.EQ.(0.0)) GO TO 4 LNG1189

IF(P.LT.(0.0)) GO TO 2 LNG1190

GO TO 1 LNG1191

2 GO TO KK , (3,4) LNG1192

3 P = P + H LNG1193

H = P LNG1194

ASSIGN 4 TO KK LNG1195

GO TO 1 LNG1196

4 A = P LNG1197

74
B = V LNG1198

C = T LNG1199

RETURN LNG1200

END LNG1201

SUBROUTINE TCM(TMC) LNG1202

TYPE REAL NUM LNG1203

TYPE INTEGER CNT1 ,CNT2, SWITCH LNG1204

TYPE REAL MWM, INCR,KIJ,MW,MOL, LAM, LAMB LNG1205

DIMENSION VCI(6),TH(12) LNG1206

COMMON /RUN/ID(12),X(12),NAM(2,12),C12(12,12),R(12),Z(12),S(12),VS LNG1207

1(12) ,TS(12) ,US(12) ,SG(12) ,EP(12) ,LAM( 12) ,NC,MW(12) ,AIJ(12,12) ,PST( LNG1208

212),TCT(12) LNG1209

COMMON /DAT/TBI(12),VBI(12),TBIM(12),VBIM(12),C(12),SGIM(12),SIM(1 LNG1210

12),EPIM(12),PIM(12),SIN(12),VSIM(12),USIM(12),TSIM(12),DVBIM(12),P LNG1211

2D(12),PV(12),RH0(12),VBIMP(12),TTM(12),MWM,CNT1,CNT2,T0LD(12),INCR LNG1212

3(12) ,SWITCH,JPC,JPCS,JMIX, DENS, VEX, HEX, GEX,TMP,VMP,TP LNG1213

COMMON/PAR/KIJ( 8, 8),AJI( 8, 8) LNG1214

COMMON/UNITS/ITC,IPC,T,TMAX,DT,P,PMAX,DP,PS LNG1215

DATA VCI/ 1.44,1.59,2.27,3.18,4.03,4.21/ LNG1216

DO 1 I = 1,NC LNG1217

J = ID(I) LNG1218

V = VCI(J)**(2./3.) LNG1219

TH(I) = X(I) * V LNG1220

1 CONTINUE LNG1221

TTZ = 0.0 LNG1222

DO 2 I = 1,NC LNG1223

TTZ = TTZ + TH(I) LNG1224

2 CONTINUE LNG1225

DO 3 I = 1,NC LNG1226

TH(I) = TH(I) / TTZ LNG1227

3 CONTINUE LNG1228

SUM1 = 0.0 LNG1229

SUM2 = 0.0 LNG1230

K = NC - 1 LNG1231

DO 5 I = 1,K LNG1232

L = I + 1 LNG1233

DO 4 J = L,NC LNG1234

TTZ = (TCT(I)-TCT(J))/(TCT(I)+TCT(J)) LNG1235

TTZ= ABS(TTZ) LNG1236

T12 = (((((((TTZ*(-3.038))+(5.443))*TTZ)+(-1.343))*TTZ) LNG1237

1 + (0.287) )*TTZ) - (.0076) LNG1238

T12 = T12*(TCT(I) + TCT(J)) * (0.9) LNG1239

SUM2 = SUM2 + ((2.)*TH(I)*TH(J)*T12) LNG1240

4 CONTINUE LNG1241

SUM1 = SUM1 + (TH(I)*TCT(I)*(1.8)) LNG1242

5 CONTINUE LNG1243

TMC = SUM1 + SUM2 + (TH(NC)*TCT(NC)*( 1.8)) LNG1244

V = 0.0 LNG1245

DO 6 I = 1,NC LNG1246

LNG1247

J = ID(I) LNG1248

TH(I) = X(I) * YCI(J) LNG1249

V = V + TH(I) LNG1250

6 CONTINUE LNG1251

DO 7 I = 1,NC LNG1252

TH(I) = TH(I) / V LNG1253

7 CONTINUE LNG1254

TMM = 0.0 LNG1255

DO 9 I = 1,NC LNG1256

DO 8 J = 1,NC LNG1257

M = ID(I) LNG1258

N ID(J) LNG1259

NUM = (VCI(M)**(l./3.)) * (VCI(N)**(l./3.)) LNG1260

75
NUM = SQRT(NUM)

DEN = (0.5)*((VCI(M)**(l./3.))+(VCI(N)**(l./3.)))

NUM = NUM / DEN NUM = NUM** (3.) AKIJ = (1.0) - NUM

TCIJ = (1.0 - AKIJ) * SQRT(TCT(I)*TCT(J)*1.8*1.8)

TMM = TMM + TH(I)*TH(J)*TCIJ

8 CONTINUE

9 CONTINUE

TCMP = TMM + (10.0)

ICT = TPO = TMM + (10.0)

10 TR = (T*1.8)/TCMP

NUM = (2901.01) -((5738.92)*TR) +( (2849.85)*TR*TR)

1 + ((1.74127)/ (1.01 - TR))

NUM = NUM * (TR - (1.0))

IF(NUM.LT.(-180.)) DD = IF(NUM.LT.(-180.)) GO TO 11 DD = EXP(NUM)

THE STATEMENT ABOVE MAY RESULT IN AN UNDERFLOW SENSE LIGHT

ON SOME OPERATING SYSTEMS WHEN THE NUMBER NUM IS A LARGE

NEGATIVE NUMBER. THE LARGE NEGATIVE VALUE IS PROPER AND THE CORRECT ANSWER FOR DD IS ZERO.

11 TCMP = TMM + ((TMC-TMM)*DD)

TEST = (1.0) - (TCMP/TPO)

TEST = ABS(TEST)

IF(TEST.LT.(.OOOD) GO TO 12 ICT = ICT + 1

IFUCT.GT.250) GO TO 12 TPO = TCMP

GO TO 10

12 TMC = TCMP/U.8)

RETURN

END SUBROUTINE BLOCK

TYPE REAL KIJ.AJI

DIMENSION KIJ(8,8),AJI(8,8)

COMMON /PAR/ KIJ.AJI

DATA KIJ7

*0 .000000 , .293E-07 , .911E-06 , .0030498

*0. 001000, 1.088608,0. 000000,. 188E-10

*0 .001000 ,0 .001000 ,1 .098880 ,1 .078910

*.188E-10, 0.001000, 0.001000,. 8578232

*.546E-06,.136E-05, 0.001000, 0.001000

*. 9690485,0. 000000,. 541E-06, 0.001000

*1. 016231,. 9976706,. 9435714, 0.000000

*1 .000000 ,1 .000000 , 1 .000000 , 1 .000000

*0. 995000 ,1 .000000 ,1 .000000 ,1 .000000

*0. 000000/

DATA AJI/

*0. 000000,. 161E-04,.257E-06,. 0003462

*0. 001000, 1.014967,0. 000000,. 188E-10

*0. 001000, 0.001000, 1.008061, 1.004105

*.188E-10, 0.001000, 0.001000,. 9863463

* . 105E-04 , . 119E-05 ,0 .001000 ,0 .001000

*. 9987221,0. 000000,. 119E-05, 0.001000

*1 .005949 , 1 .001225 , .9968984 ,0 .000000

*1 .000000,1 .000000,1 .000000 ,1 .000000

*0 . 995000 , 1 .000000 , 1 . 000000 , 1 .000000

*0. 000000/

END

,0.001000

,.463E-06

,0.000000

,1.146026

,0.995000

,0.001000

,0.001000

,1.000000

,1.000000

,0.001000

, .197E-06

,0.000000

,1.011399

,0.995000

,0.001000

,0.001000

,1.000000

,1.000000

,0.001000

, .462E-08

, .517E-06

,1.009559

,1.287762

,1.178993

,0.001000

,0.000000

,1.000000

,0.001000

,.184E-05

,.142E-06

,1.001862

,1.024894

,.9566020

,0.001000

,0.000000

,1.000000

,0.001000,

,.120E-03,

,.535E-06,

,0.000000,

,.9868486,

,1.266327,

,0.950000,

,0.001000,

,1.000000,

,0.001000,

, .335E-06,

,.103E-04,

,0.000000,

,1.003289,

,1.025269,

,0.995000,

,0.001000,

,1.000000,

LNG1261

LNG1262

LNG1263

LNG1264

LNG1265

LNG1266

LNG1267

LNG1268

LNG1269

LNG1270

LNG1271

LNG1272

LNG1273

LNG1274

LNG1275

LNG1276

LNG1277

LNG1278

LNG1279

LNG1280

LNG1281

LNG1282

LNG1283

LNG1284

LNG1285

LNG1286

LNG1287

LNG1288

LNG1289

LNG1290

LNG1291

LNG1292

LNG1293

LNG1294

LNG1295

LNG1296

LNG1297

LNG1298

LNG1299

LNG1300

LNG1301

LNG1302

LNG1303

LNG1304

LNG1305

LNG1306

LNG1307

LNG1308

LNG1309

LNG1310

LNG1311

LNG1312

LNG1313

LNG1314

LNG1315

LNG1316

LNG1317

LNG1318

LNG1319

LNG1320

LNG1321

LNG1322

76
NBS-114A (REV. 2-8C)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBS TN-1030

2. Performing Organ. Report No. 3. Publication Date

December 1980

4. TITLE AND SUBTITLE

FOUR MATHEMATICAL MODELS FOR THE PREDICTION OF LNG DENSITIES

5. AUTHOR(S)

Robert D. McCarty

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City. State, ZIP)

American Gas Association, Inc. (see page 1).

10. SUPPLEMENTARY NOTES

H Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

Four mathematical models of the equation of state for LNG like mixtures are

presented. The four models include an extended corresponding states model, a cell

model, a hard sphere model and a revised Klosek and McKinley model. Each of the

models has been optimized to the same experimental data set which included data for

pure nitrogen, methane, ethane, propane, iso and normal butane, iso and normal

pentane and mixtures thereof. For LNG like mixtures (mixtures of the orthobaric

liquid state at temperatures of 120 K or less and containing at least 60% methane,

less than 4% nitrogen, less than 4% each of iso and normal butane and less than 2%

total of iso and normal pentane) , all of the models are estimated to predict densities to within 0.1% of the true value. The revised Klosek and McKinley model is

valid only for mixtures within the range of temperature and composition specified

above while the other three models are valid for a broader range of pressure, temperature and composition. The experimental PVTx data set used in the optimization

together with comparisons are given and listings of computer programs for each of

the models are included.

l- KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

Cell model; comparisons; computer programs; corresponding states; equation of state:

hard sphere; LNG; mixtures; PVTx data; revised Kosek and McKinley.

3- AVAILABILITY

[X] Unlimited Q For Official Distribution. Do Not Release to NTIS

Qy Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

3) Order From National Technical Information Service (NTIS), Springfield, VA. 22161

-Allls. jomiuiEiftaiiiaiiajma •"-• a«aaa«flaaAmj

14. NO. OF

PRINTED PAGES

84

15. Price

$4.00

"irnMM

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