FILE

NBSiR 77-867 \

A COMPAHISON OF MATHEMATICAL MOOELS FO

THE PREOlCTiOH OF IM DENSiTiES

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1977

Prepared for:

American Gas Associa:ion, inc.

1515 Wilson Boulevard

Arlington, Virginia 22209

Robert D. McCarty

NBSIR 77-867

A COMPARISON OF MATHEMATICAL MODELS FOR

THE PREDICTION OF LNG DENSITIES

Robert D. McCarty

'

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1977

Prepared for:

American Gas Association, Inc. 1515 Wilson Boulevard

Arlington, Virginia 22209

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

Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Contents

Page

1. Introduction . 1 2. Extended Corresponding States Method 2 3. A Hard Sphere Method 6

4 . A Revised Klosek and McKinley Method ....... 8 5. The Cell Model 11

6. Conclusions 11

7. References 13

Appendix A. Deviation Tabulations 15

Appendix B. Program Listing for the Extended Corresponding

States Model 28

Appendix C. Program Listing for the Hard Sphere Model 36

Appendix D. Program Listing for the Revised Klosek and

McKinley Model 45

Appendix E. Program Listing for the Cell Model 52

List of Figures

1. Deviations in density between data from Hiza (1976) and the

indicated model. Open circles are for the model before the

present work and the closed circles are for the same models

after the present work. The composition of the mixture is

0.806 CH. + 0.047 C^E^ + 0.048 C,Ho + 0.050 nC.H,-

4 2 6 3 8 4 10 + 0.049 N2 5 2. A plot of the correction factors (k^ and for the 115

Kelvin Isotherm 9

List of Tables

1. Volumes of Saturated Liquid of the Pure Components in

liters/mole 47

2. Correction Factor k, x 10"^ 48

'

3 3. Correction Factor k_ x 10 48

iii

A COMPARISON OF MATHEMATICAL MODELS FOR THE PREDICTION OF

LNG DENSITIES*

Robert D. McCarty

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Four mathematical models of the equation of state for

LNG like mixtures are compared. Each model has been optimized

to the same experimental data set. The experimental data

consist of over 175 new PVTx data points taken in this

laboratory. The objective of the study was to obtain a mathematical model which would predict LNG densities to within

0.1% of the true value. The extent to which the objective has

been achieved is not clear at this time. Additional experimental data are needed to resolve some discrepancies between

the present data and all models investigated to date- Computer

program listings for all four models are presented.

Key words: Computer program; density; equation of state; LNG;

mixtures ; PVTx

.

1. Introduction

The purpose of this study was to optimize and compare several different

mathematical models using the experimentally determined PVTx density data of

Haynes, et al. (1976), Haynes and Hiza (1976), Hiza, et al. (1976) and Hiza

(1976) . These data are for the liquid phase of methane, ethane, propane,

normal butane, isobutane and nitrogen and various mixtures thereof. The

temperature range of the correlations was limited (9 5-150 K) and the

pressures to those of saturation, the range of which was about 0 to 20

atmospheres. The goals of the study were to produce one or more computer

models which would predict a density of LNG (liquefied natural gas) to within

0.1% of the true value, when the temperature, pressure and composition of che

LNG are specified. The goal of predicting LNG densities with an accuracy of

0.1% has most probably been achieved. The data from the above references

include nine multicomponent (three or more components) mixtures in addition

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.
to the binary mixture data in Appendix A. One of the methods (the extended

corresponding states) predicts all of the densities to within the 0.1%

objective except in the case of the methane-nonaal butane data on page 18

and one point of the propane-nitrogen data on page 22. Haynes, et al. (1976)

estimate the uncertainty of these data to be greater than that of the other

binary data. A comparison with an independent set of mixture data (68 data

points) for mixtures of the same components due to Rodosevich (1973) resulted

in no deviations between experimental and predicted (using extended corres- ponding states) densities greater than 0,1% (see Appendix A). The Rodosevich

data include binary mixtures data for the methane-normal butane system.

The choice of models to use in this study was a difficult one, because

there are many possible models and methods to chose from. Since no mathematical model is suitable for every need and needs vary greatly from

application to application, an effort was made to choose the models to be

tested in such a way as to provide useful information to as diversified an audience as possible and still achieve the stated objective of the study. In an effort to achieve these ends, the choice of models was made on the basis

of the following criteria: popularity, degree of complexity, type of

approach and likelihood of success, with of course the likelihood of success

being the most important factor of consideration.

The models and/or methods which are considered here are: the extended

corresponding states method (Leach, 1967 and Rowlinson and Watson, 1969) ; a hard sphere model by Rodosevich and Miller (1975) ; a cell model proposed by

Echert, et al. (1967) as modified by Albright (1973) ; and a graphical method

by Klosek and McKinley (1968) . All of the optimization and testing was performed in the Cryogenics Division of NBS at Boulder, Colorado except

in the case of the cell model which was done by M. A. Albright at Phillips

Petroleum in Bartlesville, Oklahoma. The details of the optdLmization of the

cell model will be published by Albright (1976) elsewhere.

A general discussion of the performance of each model is given in the

following sections. A separate section is devoted to each model considered.

The appendicies give comparisons of calculated and experimental densities for

all the models as well as listings of the computer programs for each model.

2. Extended Corresponding States Method

This method was selected because it seemed to offer an excellent possibility for achieving the objective of predicting the densities of LNG to

within 0.1% of the true value.

The extended corresponding states method is labeled as a method rather

than a model because it differs from the customary meaning of model in that

it is not an equation of state but rather a transformation function which

2
maps the equation of state of a fluid into the equation of state of another.

The thermodynamic equations for the extended corresponding states method are developed in a paper by Rowlinson and Watson (1969) and only a very brief

description will be given here. Leach (1967) developed transformation

functions for hydrocarbons which are called shape factor functions. Mollerup

(1976) and Mollerup and Rowlinson (1974) combined the earlier work with the

equation of state for methane by Goodwin (1974) to produce a computer program

to calculate the density of LNG mixtures. This method for calculating the

densities of LNG was estimated by Mollerup (1975) to be accurate to 0.1%;

however, a copy of the computer program obtained from Mollerup produced

densities for LNG-like mixtures which are as much as 3% different from those

measured in this laboratory. Figure 1 shows the deviations between the

densities from the computer program of Mollerup and the PVTx measurements

mentioned earlier. The open circles represent deviations using the Mollerup

(1976) computer program and the solid circles show deviations for the same data points using the computer program given in Appendix B, i.e., the same program after optimization to the new data.

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

based on the extended corresponding states method is an extensive revision

of the Mollerup program.

The extended corresponding states method is defined by the following

equations

:

Zi[P,T] = Z^[P h,,^^/f,.^^, T/f.,^^] (1)

^it^'^^ = fii,o ^ot^ hii,o/fii,o' ^/fii,o^ - ^^(^ii,o^ ^2)

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

pressure and T is temperatiore . 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

11, O 11,

o

allow extension of the method to mixtures. The two defining equations (1)

and (2) are necessary since there are two transformation functions. In this case the equation of state for methane by McCarty (1974) was chosen for the

reference fluid. During the course of the study it was necessary to modify

the equation of state by McCarty (1974) . The equation of state was modified

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.

3
The f . . and h. . are defined as

3.x, O 2.2.,

O

f . . = (T^./t'^) 9 . . (T ,V ) ii,o IV o 11, o r' r'

and

where

hi,o = 1 + - w^) [a3_ - a^ In + (a3 - (V^^ - Sg) ] (5)

and

*ii,o = ;! 1 * - w^) [b,(V^ - b^) - b3(V^ - b,) in ] (6)

u ^1 11

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

^ c ^

^ and = V/V^^) and is a fluid dependent parameter estimated using

experimental data. The ^j's and b^'s are fluid independent parameters,

estimated with experimental - data and the Z*^/Z? is the ratio of the compressibility factors at the critical point. The parameters a ^ , b ^ , w^ and Z^^^ are given in Appendix A. 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

^,o =.

I ] -i-j \j,o

^x,o \,o =

I ] -i-j ^ij,o '^ij.o

1/2

-o 33, f.. = (f.. f.. o')^^^ - (9) i:,o ^13 11,

r

^ij,o - ^ij ^2 ^ii,o * 2 ^jj,o>

The and the n^j are binary interaction pareimeters determined by least

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

in Appendix A. 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

4
4

CORRESPONDING STATES

0.4 .

0.2

0

0.2 -

0.4

0.6

Q.3r

0.6

0.4

0.2

0

0.2

0,4

-0-6

0.4

0.2

100

(al

HARD SPHERE

lb)

KUSEK & Mckinley

(CI

I CELL MODa

•0.2-

-0 4 - Id) noTEMPERATURE. K

120

c

0

-K

fir 0 4J

0-1 -H — (0 01 •a (U o

oe e

o

he tn

OJ u o

* (0 0) o J=

El nU O

<i-( o a

OJ •a _ M J u

H3 OS WO

01

0} u p

c *

rc he se o

-H OJ o u

c C

0) 10 OJ U

OJ a. z

.Q o rk O

>i o !-l 03 P 3 1) o

•H i-H P O

to (U -iJ IM o

c T3 /-

ITJ 01

a; 0

E

3 1-( +

-a 01 01

0) r-f OJ o

c -o u

-w <u a. T3 a u 0

31 (T3 0) £

c 0 c

o H P

•H -o s o

u c <U <t3 in

(0 -H u 01 o

•H 0 > 0) u-l 23 o

0) Q u 0 +

(U3

&4

5
set to within +0.1% except for some of the systems containing butane which

are strongly suspected to be in error. Since only binary systems data were

used as input to the method , the calculated densities for multicomponent

data are, in a sense, predictions on the part of the method.

Figure 1 gives a comparison of the extended corresponding states method

before and after modification.

Unfortunately the method has some deficiencies. The method is complex

and is not easy to use even with the aid of a computer. Figure 1 shows that

it does not perfoxrm well when insufficient experimental data are available

as input since all of the other models tested show deviations which are much

less than those in figure 1 when- tested before optimization , i.e., as they were taken from the literature. On the advantages side of the comparison,

this method has the most versatility, it handles nitrogen as a component in

any concentration, it has the widest PVTx range of any of the methods, and

it is probably the most accurate for the calculation of densities . It can

also be used to calculate other thermodynamic properties including phase

equilibria.

A comparison between the data of Rodosevich and predictions by the

extended corresponding states method resulted in no deviations greater thoin

0.1%. These comparisons were made before any of the Rodosevich data were

used as input to the optimization process. The CH^-nC^H^Q and the CH^-iC^H^|

data of Rodosevich were used in the final optimization of the corresponding

states model. A complete tabulation of deviations between the various

models and the Rodosevich data is given in Appendix A.

This method was selected for consideration since it currently enjoys wide

popularity. The model of Rodosevich and Miller (1975) is one of many modifications of the Longuet-Higgins and Widom (1964) 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 (1975) is

where the y = b/4V and a, b, and c are adjustable parameters, the PVT and R

have the usual meaning. The equation is applied to mixtures by assuming the

one-fluid theory and applying the following combining rules.

3. A Hard Sphere Method

PV _ 1 y -I- y a RT , , ,3 " RTV (11)

am

Z Z i j

(12)

6
bm

S Z b. j x.x (13)

13 > •> (14)

The mixing rules are:

1:

bM3 + b^/3 11

1:

a . = a . a . . 1: 11

(1 - j,.)

1/2

c . . + c . .

?ii'=:j J

1/2

(1 - k. .

)

i3

(15)

(16)

(17)

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

parameters. The a's, b's, c's, and k^^

' s are given in Appendix B The excess volume is now calculated using, the equation of state and

= ^m - ^ ^i^i (18)

where and the ^^ are calculated via the equations 11 through 17 and then

(19) ^m = ^ ^i^i *

where the V_ is from equation (18) and the V. are from experimental data.

The 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 (1975) and only

the and k^^

' s have been revised on the basis of the present new data

set, and only binary systems data were used to estimate via least squares the

j.^'s and k..'s. An attempt to optimize the a, b and c parameters for each

pure fluid was made using the new pure fluid data; however the results were disappointing. No appreciable improvement in the prediction of mixture

densities was achieved. The results did indicate, however, that any substantial improvement over the a, b and c values given by Rodosevich and Miller

(1975) will require some sort of temperature dependence for those parameters.

Figure 1 gives deviations between calculated and experimental densities

for the same mixttires but with different parameters for the model as the

mecins of calculating the densities. The open circles show deviations between

calculated and experimental densities before the model was optimized using

7
the present data set. The closed circles represent the deviations for the

same data points after optimization. Only binary system data were used in

the optimization process. A table of deviations between experimental

densities and those calculated via the hard sphere model is given in

Appendix A. The hard sphere model as applied here has some disadvantages when applied

to the present problem. The most serious disadvantage is that it is an excess properties method, and therefore when temperatures of the mixture

approach the critical temperature of one of the component fluids the method

fails. Since the critical temperature of N2 is about 126 K, calculations

for mixtures containing N2 are limited to temperatures below aibout 120 K,

however at temperatures where the critical temperature of a component does

not present a problem, the method works very well. The model is neither the

most accurate nor the simplest model investigated, but based on the experience

of this study, it is probably the most reliable to extrapolate.

4. A Revised Klosek and McKinley Method

This method (Klosek and McKinley, 1968) is included in the study because

it is currently very popular and it seemed at the outset to perform aibout as well as any of the others chosen. In addition it is one of the easiest

methods to apply.

This method 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 (1968) is as follows:

V„. = Z X.V. - kX-„ (20) mix X X CH^

where V^^^ is the volume of the mixture, and are the mole fraction and

volume of the ith component, X^_ is the mole fraction of methane and k is a correction factor obtained from a table or graph. The 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 N2 was present in greater than 5% concentration. Figure 2 shows

a typical isotherm for k. 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 (cOaout 4.5%), the method was modified by adding a term
O lO <M 00 ^ ^

CM r-«

O

O 9
to take into account the nitrogen when it is present. The equation becomes

^mix = ^ ^i^ - t'^l ^ -

'^l) JSl/-°^25] X^g^ (21)

where everything is the same as in equation (20) except the k^^ is read from one curve and ^2 is read from the other. Appendix D gives tables of values

for the V^, and ^2 which are spaced such that linear interpolation is

adequate in both variables (i.e., temperature or molecular weight). Using

the experimental data it was possible to calculate k directly for the 105,

110, 115, 120 and 125 kelvin isotherms only. A comparison of the linear

extrapolation of k to both lower and higher temperatures indicated the

extrapolation to be unsatisfactory. Consequently values of k for the 90,

95, 100, 130, and 135 K isotherms were calculated using the extended

corresponding states model in section 2.

In the process of calculating k for these additional isotherms it was discovered that for mixtures containing only methane-ethane and propane a table of k's could be constructed to give values for density almost identical

to those of the corresponding states model in section 2, but when either

butane or nitrogen were added k became composition dependent; Consequently,

it was decided to construct the k^ and k.2 tables in Appendix C such that

they would give results similar to the corresponding states method for

methane-ethane and propane mixtures and give the best results for mixtures

containing the butanes where the concentrations of the butanes were 5% or less

(total) and where the concentration of nitrogen is also less than 5%. The

computer comparison of the two models also revealed the following limitation.

For the model to predict LNG densities to an accuracy of 0.15% or better, the

mixture must contain 80% or more methane and less than 5% butane and nitrogen.

Figure 1 allows a common basis of comparison with the methods given in

the other sections. The open circles represent the deviations before

optimization and the solid circles show deviations after optimization. The

optimization for this model was accomplished with multicomponent data as well

as binary mixture data. An extensive tabulation of deviations between

calculated and experimental densities is given in Appendix A. For the purpose of calculating the density of LNG like mixtures, the revised

Klosek and McKinley method presented here has one very real advantage over all

the others, and that is, it is simple. It is quite easy for almost anyone to use the tables in Appendix C to arrive at an LNG density using only pencil

and paper. This is not true of any of the other methods. The value of

density arrived at in this manner will be within about 0.15% of the true

value in the worst case, and if the composition of the LNG has little or no butane or nitrogen in it, the density will be much better, on the order of

10
0.1% of the tr^-ie value. There are, however, sorrie disadvantages. It does

not handle nitrogen or butane as a component as well as some of the other

methods and if over 5% of eizher nitrogen or butane is present, it departs

rapidly from measured values. It is not as accurate as the extended

corresponding spates method and it does not extrapolate well.

5. The Cell Model

The cell model considered here was originally proposed by Renon, et al.

(1967) . In a paper by the same three authors which appeared simultaneously

(Eckert, et al. , 1967), the cell model was applied to mixtures via Scort's

(Scott, 1956) two-fluid theory and a three parameter corresponding states

theory. Albright (197 2) further modified the method by modifying the mixing

mles on the basis of a proposal by Yuan (1971) and by inserting a pressure

dependence based on the experimental liquid ethane data by ?cpe (1971)

.

As mentioned in the introduction, the optimizarion of this method was carried out by M. Albright (1976) at Phillips Petroleum Company m

Bartlesville, Oklahoma and the details of this work will be published

elsewhere. A listing of the optimized computer program together wiih a comparison with the experimental data are given :.n Appendices Z and A

respectively

.

Figure 1 shows deviations between densities calculated using the cell

model and experimental densities. The experimental densities are those

used in the comparisons in the previous sections.

5. Conclusions

As stated earlier the objective of chis study was to produce one or more mathematical models which will predict zhe density of LUG to within

0.1% of the true value. This ob;ec-ive has mosr probably been achieved as

is demonstrated by the ability of the models to predict the experimental

PVTx dara for LNG-like mixtures to within 0.1%; however all of the four

models have been fit to the data of Haynes, et al. '1976; who report thar

their daca may have as much as 0.05% systematic error. Therefore, it is

es-imazed tha-c ihe densities of LNG-like mixtures as calculated from any one

of z'-e four models given here will be within 0.15% of the -crue density for

that mixture.

Each of the models has its particular advantages and disadvantages. The

extended corresponding states model has the widest range of pressiire,

temperature and composition and is probably the most accurate, but it is

complex and difficult to use. The revised Klosek and McKinley method is the easiest to use but it is

severely limited in range of composition and temperature (i.e., less than

5% nitrocen or butane;

11
The hard sphere model works well but is limited to temperatures below

120 K for mixtures containing nitrogen.

The cell model also works well, but does not handle nitrogen at high

concentrations (30% or more) as well as the extended corresponding states,

and is only slightly less complex.

The last page- of Appendix A is a comparison of the performance of

various models for actual LNG compositions. The comparison shows that the

models perform equally well until the concentration of the butanes exceeds

4%. The largest disagreement between models occurs for the mixture which

contains a total of 4.3% of iC^H^^Q and nC^H^Q where the difference between

the cell model and the revised Klosek and McKinley method is 0.2%.

All of the other predictions for the other four compositions are within

0.11% of each other, and one of these mixtures includes 2.6% of the butane.

It is true that all of these methods were optimized using the same data set,

but the methods do differ radically in some cases and one of them

(corresponding states) does agree well (0.1%) with the Rodosevich data which

represents an independent check. Unfortunately an exhaustive search of the

world's literature has not revealed any additional experimental data of

compositions which are of interest here and which are of sufficient accuracy

and precision to be of use in this correlation, either as input data or as an independent check.

More measurements of LNG like multicomponent mixtures have been

scheduled to more precisely determine the concentration limits of nitrogen

and butane.

At the request of sponsor, the pentanes (iso and normal) have been

added as a possible component in the mixture. These components have been

added on the basis of the pure fluid data of Orrit and Olives (1974) only,

and no estimate of accuracy of the calculated density for mixtures containing

pentane is possible.

12
7. References

Albright, M. A., Private commiinication (1976).

Albright, M. A. , A Model for the Precise Calculation of Liquefied Natural Gas

Densities, NGPA Technical Publication TP-3 (197 3) . Eckert, C. A., Renon, H. and Prausnitz , J. M. , Molecular Thermodynamics of

Simple Liquids, lEC Fund 6_, 58 (1967) . 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).

Eaynes, W. M. , Hiza, M. J. and Frederick, N. V., A Magnetic Suspension

Densimeter for Measurements on Fluids of Cryogenic Interest, Review of

Scientific Instruments 4_7, No. 10, 1237-50 (Oct 1976).

Haynes, W. M. and Hiza, M. J. , Measurements of the Orthobaric Liquid Densities

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

Thermodyn. , in press, 1976.

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, in preparation, 1976.

Hiza, M. J., Private communication on Orthobaric Liquid Densities of

Multicomponent Mixtures, 1976.

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) . Leach, J. W. , Molecular Structiire Correction for Applying the Theory of

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

Thesis, Rice University (1967)

.

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

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

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).

Mollerup, J. and Rowlinson, J. S., The Prediction of Densities of Liquefied

Natural Gas and of Lower Molecular Weight Hydro^carbons , Chem. Engng.

Sci. 29 (1973) . Mollerup, J. , Correlated and Predicted Thermodynamic Properties of LNG and

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

20, 172 (1975) .

13
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)

.

Pope, G. A., Calculation of Argon, Methane and Ethane Virial Coefficients at

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

.

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

Simple Liquids, lEC Fund. £, 52 (1967)

.

Rodosevich, J. B. and Miller, R. C. , Calculation of LNG Excess Volumes by a Modified Hard-Sphere Model, Adv. Cryog. Eng. 19, 339 (1974).

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

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

.

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 Extensipns, Chem. Engng. Sci. 24_, 1565 (1969) . Scott, R. L., J. Chem. Phys. 25, 193 (1956).

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

Binaries in the Cg-C^ Hydrocarbon Boiling Range of Conformal Solution

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

.

14
Appendix A. Deviation Tabulations

The deviations tabulated below have been calculated in every case using

the following convention:

% Deviation = 100 (D - D , ) /D

exp cal exp

where D is density in moles/liter, the subscripts exp and cal stand for

experimental, and calculated via the model indicated. No entry is given for

a particular model when the calculation is not appropriate for that model.

In the case of the corresponding states model there is a deviation

tabulated for every data point. For the hard sphere model no deviations are tabulated for the pure fluid data points because the method is an excess volume method and other models were used to calculate the so called ideal

volume, i.e., V^^^^^^ = Z X^V^ (see Appendix B) . For the revised Klosek and

McKinley method deviations have been tabulated for only those mixture data

points which contain methane and have less than 5% nitrogen. This is also

an excess volume method and the calculation of the ideal volume is outlined

in Appendix C.

Saturated Liquid Ethane

(Molecular Weight 30.07012)

Experimental % Deviation

'ressure Density Temperature Corresponding Hard Revised Cell

atm mol/l K States Sphere Klosek Model

and

McKinley

0.000 21. 3408 100. 0.02 -0.07

0. 000 21. 1585 105. 0.01 -0.03

0.001 20.9746 110. 0. 00 -0.00

0. 002 20.7927 115. 0.00 0.01

0.004 20.6022 120. -0.03 0.05

0.007 20.4186 125. -0.02 0.05

0.013 20. 2317 130. -0. 02 0.04

0.023 20. 0461 135. -0.00 0.02

0.038 19. 8566 140. 0.00 0.00

Saturated Liquid Propane

(Molecular Weight = 44.09721)

0. 000 16.3065 100. 075 0,01 -0.07

0. 000 16. 1872 105. 075 -0.01 -0.01

0.000 16. 0718 110. 075 -0.01 -0. 01

15
Satiirated Liquid Propane (Continued)

(Molecular Weight = 44.09721)

Experimental % Deviation

Pressure Density Temperature Corresponding Hard Revised Ceil

atm mol/l K States Sphere Klosek Model

and

McKinley

0. 000 15.9557 115.075 -0.00 0.03

u • u u u 120.075 0.01 n AO U . (J J 0.000 15.7250 125.075 0.01 0.04

0.000 15.6085 130.075 0.01 0.03

0.000 15.4910 135.075 -0.00 0.03

0.000 15.3751 140.075 0.00 -0.00

Saturated Liquid Normal Butane

(Molecular Weight = 58.1243)

0.000 12.6517 •135.075 -0.03 -0.01

0.000 12.5706 140.075 -0.02 0.01

0.000 12.4920 145.075 0.01 -0.00

Saturated Liquid Isobutane

(Molecular Weight = 58.1243)

0.000 12.7305 115.075 -0.01 -0.01

0.000 12.6489 120.075 -0.00 0.00

(J • u u u • 3 0 O / 125.075 0.02 —ft ftft 0.000 12.4850 130.075 0.01 0.02

0. 000 12.4015 135.075 -0.00 0.02

0.000 12.3215 140.075 0.02 . -0.01

0.000 12.2353 145.075 -0.01 0.01

Saturated Liquid Nitrogen

(Molecular Weight = 28.0134)

5.257 25. 6624 95.075 0.02 0.05

7.715 24.6207 100.075 -0.02 0.00

10.744 23.4841 105.075 0.01 -0.08

14.544 22.1840 110.075 0.00 0.06

19.222 20.6490 115.075 0.01 1.93

21.927 19.7356 117.575 0.02 5.22

24.898 18.6525 120.075 0.02 8.64

16
Methane-Ethane Mixtures

0.35457 CH^ + 0.64543; C2Hg

Experimental % Deviation

'ressure Density Temperature Corresponding Hard Revised Cell

atm mol/Z K States Sphere Klosek Model

and

McKinley

0 . 23.1032 105. -0.07 -0.05 -0 . 04

0.387 22. Sill 110. -0.05 -0.04 -0.05

0.572 22.6478 Tie 115. -0 . 03 -0.02 -0.05

0.815 22.4035 120. -0. 07 -0 . 06 -0.11

1.131 22.1872 125. 0 . 03 0 . 04 -0.02

1.53 21.9441 130. 0 . 02 0.03 -0.03

0 . 49325 CH. + 0.50675

4 ^2«6

0. 321 23.9619 105. 0.07 0.07 0.10

0. 496 23.6937 110. 0.03 0.03 0. 03

0. 739 23.4328 115. 0.03 0.01 0. 01

1.06 23.1559 120. -0.03 -0.02 -0.06

1.49 22.8933 125. -0. 00 0 . 00 -0.04

2.02 22.6290 130. 0.03 0 . 04 -0.01

2.69 22.3581 135. 0. 05 0 . 06 0.02

3.51 22.0765 140. 0. 04 0 . 05 0.03

0.68006 CH^ + 0.31994 *=2"6

0 . 411 25.1027 105. 0.07 0.05 0.09

0.637 24. 7802 110. 0.01 -0.01 0 . 04 0.00

0.950 24, 4612 115. -0.03 -0.04 0. 00 -0.04

1. io 24.1402 120. -0.05 -0.06 -0.02 -0.06

1.90 23.8212 125. -0.05 -0.05 -0.01 -0.05

2.59 23.5007 130. -0.02 -0.01 0.02 -0. 00

Methane Propane Mixtures

0.29538 CH^ + 0.70462 <=3«8

0.267 18.5132 105. -0.12 -0.08 -0.08

0.404 18.3624 110. -0.12 -0.09 -0.12

17
0.49637 CH^ + 0.50363 C^H

Experimental % Deviation

'ressure Density Temperature Corresponding Hard Revised Cell

atm mol/£ Klosek Model

McKinley

0.379 20.4909 105. -0.03 0.01 0.02

U . JO"* 20.3046 110. -0.03 0.01 —U . UX

0.863 20.1180 115. -0.02 0.01 -0.03

1.23 19.9311 120. 0.00 0.01 -0.04

1.700 19.7471 125. 0.04 0.03 -0.02

2.29 19.5546 130. 0.05 ^ 0.01 -0.03

0.74920 CH. + 0.25080

4 ^3^8

0.472 23. 4768 105. -0.02 0.02 -0.11 0.02

23.2064 110. -0.03 0.00 -0.13

1.085 22. 9364 115. -0.02 -0.00 -0 . 13 -0.03

1. 561 22. 6665 120. 0.01 0.01 -0.12 -0.01

2.187 22. 3818 125. -0.01 . -0.04 -0.16 -0.03

2. 989 22.1019 130. 0.01 -0.05 -0.14 -0.01

0.85796 CH. + 0.14204

4 ^3«3

0.510 24.9622 105. 0.07 0.10 -0.02 0.09

0.791 24.6331 110. 0.06 0.08 -0.03 0.07

1.133 24.2941 115. 0.03 0.04 -0.08 0.03

1.70 23.9491 120. -0.00 -0.00 - .11 0.01

2.383 23.5941 125. -0.05 -0.06 -0.19 -0.02

3.257 23.2461 130. -0.04 -0.06 -0.19 0.01

Methane Normal Butane Mixtures

0.91674 CH4 + 0.08326 ^^4^10

.514 25. 1536 105. 0.23 0. 25 0. 16 0.30

.799 24. 7960 110. 0.15 0. 16 0. 09 0.16

1.200 24. 4512 115. 0.15 0. 14 0. 08 0.10

1.730 24. 0910 120. 0.11 0. 08 0. 04 0.00

2.440 23. 7370 125. 0.12 0. 08 0. 05 -0.03

3.330 23. 3789 130. 0.15 0. 08 0. 06 -0.04

4.450 23. 0110 135. 0.17 0. 08 0. 09 -0.04

5.810 22. 6391 140. 0.21 0. 10 0. 21 -0.02

18
0.58828 CH. + 0.41172 nC-H.^

4 4 10

Experimental % Deviation

Pressure Density Temperature Corresponding Hard Revised Cell

atm mol/i K States Sphere Klosek Model

and

McKinley

1. 615 18 . 6495 120. 0.00 0.00 0 . 09

2.251 18.4772 125. -0.02 - .02 -0. 05

2.251 18.4853 125. 0.03 0.03 -0.01

3.141 18.3058 130. -0.03 -0.07 -0.19

Methane Isofautane Mixtures

0.48687 CH. + 0.51313 iC.H.-

4 4 10

0. 621 17 . 3575 110. 0.02 0.07 -0 . 02

17 2076 115. -0.01 -0.00 -0 05

1.343 17.0639 120. -0.01 -0.03 -0.03

1.328 16.9156 125. -0.03 0.10 -0.03

Methane'-Nitrogen Mixtures

0. 95248 CH. + 0.04752 N4 2 1. 36 26. 8476 105. -0.03 -0.05 -0. 06 -0 . 05

1.96 26 . 4052 110. 0.04 0.00 0 . 04 0 . 00

2.600 25.9374 115. 0.05 0.01 -0.07 0.02

3.45 25.4522 120. 0.06 failed -0.02 0.03

125. 0.07 failed LI . U *s 5.75 24. 4210 130. 0.04 -5.69 0.02 0.03

7. 20 23. 8600 135. -0.03 -4.00 0.01 -0 . 01

9. 08 23. 2809 140. -0.07 -2.69 -0.02

0. 69651 CH. + 0.30349 N4 2 3.40 26.8735 100. -0.00 0.06 0.09

ft • 0 uu ^ 0 • J J7 ^ 105. 0.04 0. 02

6.100 25. 7686 110. -0.00 -0.05 -0.02

7.91 25.1790 115. -0.03 0.13 -0.08

9. 980 24.5737 120. -0.04 1.88 -0.07

0. 50758 CH^ + 0.49242

3.260 27.0801 95. 0.04 0.08 0.13

4. 59 26.4588 100. 0.02 -0.05 0.04

6.29 25.8106 105. -0.02 -0.18 -0.06

8.33 25.1387 110. -0.05 - .21 -0.10

19
0.50758 CH^ + 0.49242 (continued)

Experimental

Pressure

atm

Density Temperature

K

% Deviation

Corresponding

States

Hard

Sphere

Revised

Klosek

and

McKinley

Cell

Model

10.83

13.800

17.08

20.820

24.4431

23.7096

22.9315

22.1005

115.

120.

125.

130.

-0.03

•0.03

•0.01

0.08

.24

3.37

failed

-2.29

-0.05

0.07

0.25

0.05

0.000

0.000

0.000

0. 000

18.619

18.4646

13.3059

18.1509

Ethane-Propane Mixtures

0.67287 C2Hg + 0.32713 C^Hg

125.

130.

135.

140.

0.00

0.01

0.00

0.02

,02

,02

,01

,01

-0.02

-0.00

0.00

0.05

0.50105 C_H, + 0. '49895 C-,H,

0. 000 18. 3618 105. 0.02 0. 02 0. 04

0. 000 18. 2169 110. 0.00 0. 01 0. 00

0. 000 18. 0726 115. -0.01 -0. 00 -0. 02

0. 000 17. 9282 120. -0.01 -0. 01 -0. 04

0. 000 17. 7880 125. 0.00 0. 00 -0. 03

0. 000 17. 6412 130. -0.02 -0. 02 -0. 04

0. 000 17. 4988 135. -0.01 -0. 01 -0. 01

0. 000 17. 3526 140. -0.01 -0. 03 0. 00

Ethane Normal Butane Mixtures

0.65343 C2Hg + 0.34657

0. 000 17. 2184 115. 0.00 -0. 00 0. 00

0. 000 17. 0824 120. -0.01 -0. 02 -0. 03

0.67117 C^^Q + 0.32883

0. 000 17.5047 110. 0.00 -0.00 0.01

0. 000 17.3706 115. 0.00 0.01 -0.00

0. 000 17.1031 125. 0.01 0.02 -0.01

0. 000 16.9626 130. -0.02 -0.01 -0.04

0. 000 16.8285 135. -0.01 -0.00 -0.01

0. 000 16.6947 140. 0.01 0.00 0.03

20
Ethane Isobutane Mixtures

,68939 C2Hg 0 31061 iC.H,

-

4 10

Experimental

Pressure Density Temperature

atm mol/i

Corresponding

States

% Deviation

Hard

Sphere

Revised

Klosek

and

McKinley

Cell

Model

0. 000

0.000

17. 3716

17.2344

115.

120.

-0.00

-0.02

-0.01

-0.03

-0. 03

-0.05

0.000

0. 000

0.000

0.000

17.9779

17.8401

17.4235

17.2825

0.72436 C_H^ + 0.27564 iC.H,-,

2 6 4 10

105.

110.

125.

130.

0.00

0.01

0.01

0.00

0.01

0.01

0.01

0.00

0.00

-0.01

-0.01

0. 00

Ethane Nitrogen Mixtures

3.800

4.57

5.400

6.300

21.4718

21.2912

21.0845

20.8998

0.94067 C2Hg 0.05933

105.

110.

115.

120.

-0.03

0.03

-0.04

0.00

-0.02

0.03

-0.01

-0.72

-0. 01

0.03

-0.03

0.02

0.000

0.000

0.000

14.6839

14.1748

14.0786

Propane Normal Butane Mixtures

0.58692 C^Hg + 0.41308 nC^H^Q

110.

135.

140.

0.01

-0.03

0.00

0.02

-0.03

-0.00

0. 04

•0. 06

•0.02

0.000

0.000

0.000

14.1343

14. 0333

13.9345

0.60650 C^Hg + 0.39350 nC^H^g

140,

145.

150.

-0.00

-0.00

0.02

-0.00

-0.00

0.02

02

00

05

0.000

0.000

14. 6487

14.5521

0.60949 C3Hg + 0.39051 nC^H^^Q

115.

120.

-0.01

0.02

-0.01

0.02

02

00

21
Propane Isobutane Mixtures

0.49030 C ^Hg + 0.50970 iC4^10

Experimental % Deviation

Pressure Density Temperature Corresponding Hard Revised Cell

atm mol/Z K States Sphere Klosek Model

and

McKinley

0.000 14.3080 105. -0.01 -0.01 -0. 02

0.000 14.2136 110. -b.oi -0.01 -0. 03

0.000 14.1219 115. 0.02 0.02 -0.02

0.000 14.0257 120. 0.01 0.01 -0.03

0.000 TO Q 0 n A IOC 0.00 A A A -0.03

0.000 . 13.8342 130. -0.01 -0.01 -0.02

0.50326 C ^Hg + 0.49674 iC'4^10

0. 000 13.9718 125. 0.01 0.01 -0. 02

0.000 13 . 8737 130. -0.01 -0.01 -0.02

Propane Nitrogen Mixtures

0.93260 C^Hg + 0.06740 ^2

6.230 100. 0.01 0.04 -0.08

8.680 16.7084 105. 0.18 0.20 0.05

0.96206 C^Hg + 0.03794 ^4.

4.890 J.O « 4 O J O 105. 0.01 0.02 -0.06

6.620 16.3410 110. -0.00 0.00 -0.10

\ 0.97986 C^Hg + 0.02014 ^2

3.520 16. 2131 110. -0.01 - -0.01 -0.07

4.650 16.0931 115. -0.02 -0.02 -0.10

Normal Butane Isobutane 1Mixtures

0.52961 nC,H,. + 0.47039

4 10 iC 4^10

rt riCirt U • UUU 12.6943 125. -0.01 -0.01

0.000 12.5133 130. 0.01 / 0.01 -0.01

0.000 12.5271 135. -0.01 -0.01 -0.04

0.000 12.4447 140. 0.00 0.00 -0.02

22
Comparison of Models to Rodosevich Data

Experimental

Density Temperature

mol/Z K

0.9478 CH. + 0.0522 C-,H,

4 2 6

Corresponding

States

% Deviation

Hard

Sphere

"Revised

Klosek

and

McKinley

Cell

Model

27. 7678

27.0621

26.4026

25.7573

91.09

100.01

108.08

115.60

-O.Off

-0.02

-0.02

-0.04

-0.04

-0.06

0.06

-0.07

0.01

0.01

0.02

0. 02

-0.01

-0.05

-0.06

-0.06

0.8516 CH^ + 0.1484 €2^^

27.1003

26.4711

25.8859

25.3620

91.01

100.01

108.02

115.13

-0.04

-0.01

-0.05

-0.02

-0.09

-0. 05

-0.08

-0.05

•0.00

0. 05

0. 02

0. 07

-0.01

-0.01

-0.06

-0.03

26.4131

25.8398

25.3235

91.13

100.01

108.01

0.7528 CH. + 0.2472 C-H,

4 2 5 -0.01

-0.05

-0.03

-0.05

-0.08

-0.06

0. 03

•0.02

0.01

0.05

-0.03

•0.04

26.0647

25-0144

24.5712

91.00

108.00

115.00

0.7026 CH. + 0.2974 C-H,

4 2 6 -0.03

-0.09

-0.09

-0.07

- .11

- .10

0.01

0.06

0. 05

0. 04

0.09

•0.10

0.6909 CH. + 0.3091 C.Hj4 2 6 25.9997

25.4466

24. 9476

24.5104

91.00

100.00

108. 00

115.00

0.03

-0.04

-0.08

-0.07

-0.01

-0.06

-0.10

-0.09

0.05

•0.02

•0.05

•0.04

0.10

•0.01

0. 08

•0.09

0.9737 CH^ + 0.0253 C^Hg

27.6870

26. 9709

26.3352

25.7294

90.99

100.03

107.87

114.99

-0.01

-0. 01

-0.02

0.02

-0.02

-0.03

0.00

-0.00

•0.03

0.03

0.00

0. 01

0.01

0. 04

0.02

0. 01

23
Experimental

Density Temperature

mol/l K

0.9262 CH^ + 0.0738 C^Hg

Corresponding

States

% Deviation

Hard

Sphere

Revised

Klosek

and

McKinley

Cell

Model

26.9121

26.2667

25.6819

25.1553

91.01

100.06

108.01

114.97

0.01

0.02

0.03

0.04

0.03

0-03

0.03

0.04

-0.02

-0.01

-0.01

0.01

0.05

0.03

0.02

0.04

26.4774

25.8692

25.3165

24.8207

91.02

100.05

108.01

114.98

0.8997 CH^ + .1003 C3Hg

-0.02

-0.01

0.01

0.03

0.01

0.02

0.02

0.04

-0.06

-0.06

-0.06

-0.04

0.04

0.02

0.01

0.03

0.9506 CH. + 0.0494 nC.H,.

4 4 10

26.5731

26.2075

25.6121

25.0771

95.00

100.00

108.00

115.00

0.03

0.01

-0.01

-0.02

0.04

0.01

-0.02

-0.04

0.00

-0.01

-0.03

•0.03

0.13

0.06

-0.03

-0.09

25.3126

24.9776

24.4906

0.9206 CH. + 0.0794 nC.H,.

4 4 10

103.00 -0.00 0.02

108.00 0.01 0.02

115.00 0.00 -0.01

-0.07

•0.06

0.07

0.09

0.04

-0.05

25.4233

26.0010

24.8843

108.00

100,00

115.00

0.9462 CH^ + 0.0538 iC^H^^Q

-0.00

-0.03

-0.04

-0.01

-0.01

-0.08

•0.21

•0.22

•0.26

0.17

0.10

0.18

0.9152 CH. + 0.0848 iC.H-„

4 4 10

25.5931

25.2653

24.7274

24.2436

95.00

100.00

108.00

115.00

0.03

0.03

0.02

0.01

0.09

0.07

0.02

-0.04

-0.23

-0.26

-0.30

-0.34

0.20

0.21

0.25

0.30

24.'
0.8466 CH^ + 0.1025 C^Hg + 0.0509 C3Hg

Experimental % Deviation

Density Temperature Corresponding Hard Revised

mol/l K States Sphere Klosek

and

McKinley

Cell

Model

25.9821

25.4311

25.4273

24.9401

100.01

108.01

108.02

115.00

-0.02

-0.02

-0.03

-0.01

•0.03

•0.03

•0.04

•0.01

-0.03

-0.03

-0.04

-0.01

-0. 00

-0.02

-0.03

-0.01

24. 9240

24.4194

23.9670

0.8679 CH^ + 0.0818 C^Hg

100.00

108.00

115.00

-0.01

-0. 02

-0.02

0.0503 iC.H,.

4 10

0.04 -0.19

0.00 -0.22

-0.03 -0.25

0.12

0.12

0.14

27.3493

25.4706

26.0417

26.6667

0.8409 CH. +

4 91.00

115.00

108.00

100.00

0.1086 C2Hg + 0.0505 N2

-0.06

-0.06

-0.04

-0.05

-0.03

-0.11

-0.07

-0.06

0.10

0.03

0.02

0.10

0. 07

0.01

0.02

0.03

27.2725

25.9410

0.9055 CH. + 0.0497 C,Ho + 0.0447 N4 3 8 2 91.00

108.00

-0.03

-0.01

0.03

-0.01

0. 03

-0. 09

0.09

0.06

25.5434

25.0313

24.5507

0.8303 CH^ + 0.1001 C^E^ + 0.0493 C^Hj + 0.0203 nC^H^Q

100.00

108.00

115.00

-0.02

0.02

-0. 03

-0,00

0.03

-0.02

-0.05

-0.01

-0. 06

0.03

0.03

•0. 04

28.0702

27.2896

26.5717

25.9282

0.9488 CH^ + 0.0512 N2

91.00 -0.03 0.01 -0.08

99.99 -0.03 -0.02 -0.04

108.01 0.01 -0.02 -0.03

114.98 0.06 0.01 -0.12

0.02

•0.02

•0.02

0.02

25
0.8449 CH^ + 0.1551 nC^H2_Q

Experimental

Density Temperature

mol/2. K

Corresponding

States

% Deviation

Kara

Sphere

"Revised

Klosek

and

McKinley

Cell

Model

27.9666

27.0973

26.3387

25.6469

91.058

100.35

108.13

115.05

-0.02

-0.01

-0.00

0.06

0.12

0.04

-0.03

0.04

0.16

0.06

0.01

0.03

26
Comparison of Models for ryp:.cal i:;g Coinposi-ior.s

.

Corresponding States Model Was Taxan as a Reference

0.92834 CH, - 0.C4026 C^H- + 3.30432 C.H„

4 2 0 J 3 ^ 0.00396 iCH,. - 0.01313

% Differer.ca

Density from Temperature Hard Revised Cell

Corresponding States K Sphere Klosek Model

Method, mol/i and

McKinley

27.2677 ' 95 0.00 0.03 0.03

26.8737 100 -0.01 0.04 0.02

26.4716 105 -0.02 0.02 3.31

0.92779 C3. - 0.03115 C-H, - 0.02069 C-H, ^ 0.02037 N.

4 i o J 3 2. 26.4540 105 -0.31 0.33 0.01

26.3562 100 -O.CO 3.34 3.31

27.2504 95 0.31 0.04 0.03

3.915 CH, ^ 0.041 C-H, - 0.009 CH, -r 0.3023 nC,H.„

-r 0.0025 iC.H, Q ^0.01

27.252 95 -0.01 0.02 0.32

26.8616 100 -3.32 3.03 3.00

26.4632 105 -0.32 0.02 -0.30

0.38" CH, - 0.055 C-H- - 0.024 C-H,

4 ^ c J 3

-r 0,013 r.C_,H.|Q - 0.013 iC^H,Q - 0.007

25.6300 105 0.01 -0.C4 3.33

26.0342 100 3.32 -0.33 3.36

26.3821 95 3.33 -0.03 0.38

0.5975 CH, - 3.156 C-H, - 3.392 C,3,

4 CO J 3 + 0. 029 :^-C_,H^Q - 0.014 -C^H. ^ - 3 . C115

24.3315 95 0.03 -0.05 0.15

24.0648 _100 0.07 -0.05 0.11

23.7942 105 0.07 -0.03 0.08

27
Appendix B. Program Listing for the Extended Corresponding

States Model

The program listing that follows is for 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) . 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 atmospheres) ; T (temperature in degrees 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 amd D are interchanged, i.e., D is an input variable and

P is calculated by the program.

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

phase of any of the pure components of CH^^ , ^2^6' ^3^2' ^^^4^10' ''^4^10' ^2'

nC^H^2 °^ ^'-4^12 °^ 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.

28
SUBROUTINE PDMIX <P»OtT»X)

FOR A CALL TO PDMIA* P»T AND X ARE INPUT. ^ IS IN ATM,T IS KELVIN ANU U lb OU tP U T IN T HL UNI IS OF MOLhS/LI rE ^< FOR A CALL TO P MIXt D»T AND X ARE INPUT ANO P IS OUTPUT* THE

UNirb AWh THE SAML

THE X MATRIX MUST CONTAIN THE MQL FRACTION OF THE ALL0WA3LE FLUIDS

IN THt FOLLOWING 0RDER» l»Cl,2«C2» 3=C3*4=NC4»5alC4«6*N2

PLACE A ZERO IN THE ELEMENTS OF X WHERE THAT PARTICULAR 3AS IS NOT

PREStNf

DIMENSION ZATA(10«1Q) «ATA(l0tiQ) » TC ( 1 0 ) * VC (1 0 ) » ZC ( 1 0 ) » AC ( 1 0 ) «

W

(1 0

)

1 »PC( 10) tCF(9)

DIMENSION THETAdO^lO) » TH ( 1 Q 10 ) ^PHI (10 « 10) ,PH (10 » 1 0 ) f F (10 , 1 0 ) «FH l(10»10)»H(10»10)tHH(10»lO)»VR(10»10)»TR(lO»10)»X(10)

COMMON/DATA M/ZAT A » ATA

»

TC VC » W TCP* VCQ * ACQ * ZCO « RR*R QMEGJ » AC » ZC »N l.PC.CF —

OATA(IE=0)

D=0.0

GO TO » ENTRY PMIX - P=0.0

IP=1

GO TO 5 * IP=0

5 CONTINUE

IF(IE.GT,0)GO TO 6

IE=1

CALL OA I A CHI* IBASE=L=1

CALL '^IX DATA(IBASE)

<S CONTINUE

00 1 I=l»N

F(I»I)=H(I,I )=1.

THETAll,l)=l.

1 PHI(I»I)=l,

DO 30 J=i»30

HX=FXHX=0.0

DO 10 I=ltN

FH ( I . I ) =F ( I » I

)

HH(I,i)=H{I,I>

IF(X(I) .LT. .0001)00 T 0 10

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

H(I*I) = (VC(I>/VC(L> ) *PHI(I»I)

10 CONTINUE

DO 11 IA=I.N

UO 11 id=l»N

IF(X(IA),LT..0001)G0 TO 11 IF(X(1B).LT.. 0001)60 TO 11 FAB=ZATA(IA*IB)o(F(IA»IA)* F ( I8» IB) ) »*. 5

4AB=ArA(IA»Ia)*(.5*H(IA.rA)»»(l./3.)*,5»H(IB«IB>**(l./3,) )»»3

HX=HX*X(IA)»X(IB)»HA8

FXHX=hXrlX*X(IA>*X (IB)»HAU*KAB

11 CONTINUE

FXsFXHX/HX

PRO=P*HX/FX

TRO=T/FX

OEN=0*HX

IFdP.EQ.DGO TO 8 OD=SATL(TRO>»1000.*1.

9 0£N=FINO M(PRO ,TRO,00)

B CONTINUE

IF(OEN.L£.0.0) GO TO 33

VRO=1000./DEN

29
DO 12 l=\*H

IF(X(I) ,LT.,0001)GO TO 12

VR ( I » I ) =VRO»PHI < I , I ) /VCO

TR(I»I)=TRO*THETA(I,n/TCO

Tr{VR(I« I) .GT.2.)VR< T. T) *2.

TH < T • I ) sTHFTA ( T • I

)

THET A ( I . I ) = 1

. ( AC ( I) -OMEGO > • ( CF ( 1) -CF ( 2 ) ALOG ( TR ( 1 1 1 ) ) < CF ( 3

)

1)/TR(I»I) )*(VR(I»I)-CF(5) )

)

-CF(4^

PH(I»I)=PHI(If I)

PHI {I»I) = (1.*UC{1)-0MEG0)«(CF(6)»<VR(I»I)-CF(7) )-CF(8)«(VR(I *I)

12

1-CF(9) )«AL0G(TR(I»I) » ) )»ZC0/ZC{I)

CONTINUE

00 13 I=1»N

IF{X(I) .LT,, 0001)60 TO 13

IF{ABS < tFH(I»I)-F(I,n )/F(I,I)) ,GT,.001)GO TO 30

IF(ABS ((HH(I»I)-H(I»I))/H{I,I)),GT,,001)GO TO 30

IF(A85 ( <TH(I»I)-THETA<I»I) )/THETA(I, I) ) .GT. ,001)00 TO 30

IF(A8S ((PH(I.I)-PHI<I,I>)/PHI(I,I)).GT..001)GO TO 30

13 CONTINUE

GO TO 31

30

33

CONTINUe

PRINT 100»P»0E^J»T

100 FORMAK* ITTtRATION FAILtU Al*,3Flo.4)

STOP

31 D=oeN/HX

THC=THETA(6»6)

IF(IP.EQ.O)GO TO 32

CALL PRESS<P,DEN»TRO)

p=p«FX/HX

32 RETURN

END

SUBROUTINE MIX DATA(lBASt)

DIMENSION ZATA<10»10) .ATAdOtlO) tTCdO) tVC(lO) tZC ( 10) AC ( 10) M(10)

1,|JC< 10) tCI- (9)

COMMON/OATA M/ZATA,ATA»TC» VC»K<»TCO.VCO»ACO»ZCO»RR»R»OMEGD» AC* ZC»N

1,PC»CF

DATA (PC=45. 356 t^?. 96757 t^l. 39008 37. 79462* 36. 40753 33.10393)

OATA<TC=l90.555.305.5,370.»42b..408.1»126.2)

DATA ('<<=1 6. 04303*30. 070 12*44. 09721* 58. 1243*58. 1243* 28. 01 34)

DATA <VC=<?8. 522* 146. 2* 200.* 251. 62*263. 00*89. 827)

DAT A (AC=. 01 09*. 11 0427,. 154837*. 176372*. 150115*. 0291 791)

DATA <R=82. 05606) * <PR»8.3144) , (Na6)

DAT A <CF=-.l 09495 *.919454*-4.0l525*-4. 14192*. 444850 *.356808»

11. 026 19*. 393323*. 76 1533)

DATA (ATA ( 1*2) =1 .00514) . ( AT A < 1 * 3) »1 . 0 1 922) * ( ATA ( 1 *4) al .04454)

*

1 (ATA (1*5) =1.04931) < ATA (1*6) a I. 01009)

*

A (ATA (2* 3)

=

1.00599) , (ATA (2*4) a 1 .01616)

*

2(ATA(2*5)=1.0236'5) , (ATA (2*6) = i .02127) * (ATA(3*4) =1 .001 i^Z) * 3 (ATA (3. 5) =1.0 1140) .( ATA ( 3*6) =1 .04606) * (ATA (4*5 ) =.9971 14)

*

4 (AT A (4*6) =1.1 3889) * ( AT A (5 *6 ) =1 . 1 3889)

DATA (ZATA ( 1 *2) =1.01 127) * (ZATA ( 1 *3) ».988608) (2ATA ( 1 *4) ». 987281 )

»

KZaTAI 1*5) =.979315) ( 2aTA ( i *6) = ,'553430) (ZATa (2*3) «. 999961 ) 2 (ZATA (2*4 ) 3.972223) * (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)= .857310) , (ZATA (5*6) =.857310)

L=IBASE

N=8

N1=N-1

30
PC(7)=33.37

PC(8)=Ji.b:

TC (7) =469.6

TC(8>=460.39

VC(7)=304,

VCC«>=30b.

W(7)=72«IS139

AC(7)=. 234320

AC(d)=. 288886

ATAn»7)=ATA(lfa) = l,.04

ATA<2»/)=AIA<^,a)=l,.02

ATA(3»7)=ATA<3»8)=1,.01 ATA<4« n=ATA<4*d)=l

ATA(5»7)=ATA(5,8)=1

ATA(6» ^)=ATA(6,8)=1. —ATA(7t8)=l,

ZAI A(l» /)^ZA|A(i«tf)x.tjb

ZATA<2»7)=ZATA<2»8)»,99 —ZATA(3» n=ZATA«J,8)a.9y

ZATA{4»7)=ZATA(4t8)».99 —ZATA(5» /J=ZATA(b»«>».99

ZATA(6»7)=ZATA(6f8)»,99 —ZATAl /»8»=1.

DO 3 J=ltNl

Jl=J*l

DO 3 K=J1»N

ZATA(KtJ)=ZATA(J^K)

3 ATA(K»J)=ATA< J»K)

DO 4 I=ltN

4 ATA(I»I)=ZATA(I»I)=1.

PCO=PC(L)

VCO=VC(L)

TCO=TC(L)

OMEGO=AC{L)

ZCO=PCO<>VCQ/TCO/R

00 5 I=1»N

5 ZC(I)=PC(I)*VC(I)/TC<I)/R

RETURN

END

31
SUBROUTINE PROPS ( PP , QDt TTl OIMENSICN X(33)

DIMENSION B(33)tG(32)

EQUIVALENCE (B,X)

COHMON/OATA/G^Rt GAMMA

OATA (10=1)

OAT/r(IZ=l)

1 C6NTInU£

D=QO

P-PP

T=TT

GM=GAMMA

02=0*0

3=02*0

0Z»=03*0

05=0i»»0

06=05*0

07=06*0

08=07*0

05=0a*0

01Q=09*0

oii=oia*o

012=011*0

ai3=012*0

TS=SQRT <T)

T2=T*T

T3=T2*T

Ti^T3*T

T5=TU*T

F=EXP (GM*02)

GO TO (100^200)

eHYry pRlii

K=l

GO TO 1 IwO CONTINUE

Bt i)=02*T

Bl 2)=02»TS

3( 3i=£)2

3( ^)=02/T

a< 5)=02/T2

3( 6)=03*T

3i 71=03

a( 8)=Q3/T

81 3)=L)3/T2

a(10)=O'**T

8(11) =0'*

B (12)=0»/T

o(13)=05

B(l'*)=06/T

3(15)=06/T2

a (1&)=07/T

a<17)=0<J/T

3(18)=08/T2

a(l9)=09/T2

3(20)=03*F/T2

S<2iJ=03»FyT3

3{22)=05*F/T2

32
B(23)=0S»F/T£f

B <2'»)=07*F/T2

3 ( 251 =07*F/T3

3 I26I=G5*F/T2

a<27) =09»F/T^

B(29)=011»F/T3

8t31)=013*F/T3

a<32)=D13*F/T'»

1C2 p=a

no 1Q1 T = -1.3? 101 p=p+g<I)»S{X)

PP=P

SFTURN

ENTRY OPOO

K=? IN — GO TO 1

2 0 0 CONT TNUF

Fl=2. 0Q*F»GM*O

F21=3.QSa*F*02 •F1*D3

F22=5. 300*F*0'* +F1»05

F2<^9.0 00*F»O8 *-Fl*09

F 25=11. 3D*F*01.I1+F 1*011

F26=13. !3D*F»012*F1*013

S< 2)=2.00*O*TS

fi { 3J=?.an*n

ac «»)=2.00»O/T

3< 6)=3.C0»O2*T

S( ?i=3.(lD*05

a< A)=3.0Q»Q2/T

Bl Ml =3 . Q 2/T2

a<10)='».Qjj*O3*T

a < iiJ =4 . fl il*D 3 afi2)=i».fla*Q3/T

a (13) =5. OQ-*QAk B (IM =6. QO*0 5/T

a<16)=7.aO»06/T

9ft^f /^wVUw Wf '

1

3<18)=d.0C*Q7/T2

3 < 20 ) =F21/T2

) =F71 /T'^ 3 <22) =F22/T2

' 3 i'23r=T2"27T^"

'

'

a CZ'f »=F23/T2

3(25>=P23/T3

3{26)=F2'»/T2

a(27)=F24/T%

a<26»=F25/T2

i(^5)=?25/T3

3(30)=F26/T2

33
3(31»=F26/T3

202

00 201 1=1,32

201 p=p*-a(i»^G<i)

P=p+R*T

pp=p

ENO

SUBROUTINE OATA CH»

DIMENSION G(32)»WP{9) ,GI(11)

COMHON/DATA/GtR, GAMMA trfPt OTP

DIMENSION A(1Q)

COMMON/SATC/A

R=. 08205616

GAMMA=-.O096

A(1)=19Q.555

A{2)=13.23

A(3}=18.4a4156i»72

A(»)=7.3t»9a921512

A(5)=-l. ^313160(433

A(6)=A<7)=fl.O

G( l)=-.187a279976d5e-01

Gl 2)= .1033a7138009E+01^

G( 3)=-.l333d7626bi5e+i32

G< <»)= .772311t>7856^E-t-03

G( 5>=-.377ia330fla95e+a5

G( 6)= .8'+63188'f3<*75E-0 3 5( 71=-.4^6^i5aa/*52i5+afl

G< 8)= .a699gQ352'tli*E-*-02

S( 9) =-.322321592'»93£+05

G<1G) =-.3958 1»30 2631 aE-Ot» 6<11)= .2667723ia035£-01

G<12) =-«3G<^01C0 57839E-t-01

G(13)= .19153'»5a7536E-a3

Gllif )=-.1955a79 33U5aE-Q3

5a5)= .607i*7i567674£+0l

G (16)=-. 52960 95259a^E-a3

6(17)= .i5^26i»2a6d()'*e-!34

G(ia)=-.109d5 2ia2 8'*2E-Jl

G<ia)= .i^fl3i55if5'32'3E-(3 3 G(20l= .3S6'»70Q037'»6E + 05

S(2i)=-.i3?53a5d26i2e+a7

GC22)= .1952701t»^4aiE-t-0 3 G(23)= .165936Qai629£+07

G(2'*)= .6Q30511<»6711E>a3

b(25)= .376't851623ad£+a2

G<26»= .125593680622E-02

6(27)=-.3if3570Q325l3e+a2

G{2a)=-.54C9'»5Q9^139E-05

G(29)= .ia562223'*663£-02

G(3a)= .77Q736i792'»5E-03

G^3il=-.2aici6a3i<i&53E-J5

G(32)= .3723769616t»7E-Jt»

ENO

34
FUNCTION SATHT>

OIMENSICN A(iO)

COMWON/SATC/A

IF(T.GT.A (1) I GO TO 1 -

X=(1.-T/A(1J ) SATL=A(2) + A(3)*X»* ( .35) +A(if)»X*A{5) X** (<+./3.) +A (6) X»*(5./3.

l)*A(7)*X*-»2

SATL=SATL/130G. " RETURN

i SATL=l.£2a ' RETURN

ENO

FUNCTION FIND M(P,TtD)

00=0

TT=T

00 10 1=1, 5Q

CALL PR£S5(PP,00tTT)

P2=PP

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

OP=PP

C0RR=<P2-P)/0P

IF(ABS (CORR) -l.E-7*0D) 20,20,10

10 00=00-CORR

FIND H=li RETURN

20 FIND M=00

ENO

35
Appendix C. Program Listing 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 = RODEN(P,T,X)

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

temperature in degrees Icelvin, 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 ethcuie

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 isopentane

X(8) mole fraction of methylpentane

Note: The inclusion of the pentanes is due to Rodosevich and Miller (1975)

and no checking or optimization of parameter 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^, (^2^6' ^3^8' ^^4^10' "*'4^10 ^2* '^^^ 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 N2) 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.

36
FUNCTION ^00ENIP,T,X>

OIMENSION XHO>

CiLt F>1(0,T,X,V,3)

0 = 26. vsv+v i:elcp, c,t,x>

^OOENst 00 3 ./Y

RETURN

. END

SUBPOUTINE FM<Q,T»Xf vgtG"?)

PgEOIC TlON OF EXCESS PBQPEgiT IES WITH LHW XOTENTIAL. COmp 1-mETH

ANE»COMP ;J-e.TH&NE*CguP "J-P'^OP ANE ^ COMP 4 M- ;jU T A^E > CO^P j-I-^U T ANE» COMP 6-NlTROGEN* CQHP I SQP ENTANE CO^P a-METHYLPENT ASE

AOV CriyO tSS5. VOL. 19 {iy/3)-«E'»R0GRAH£D JY !?. mCCaP I Y , 2/22/74

APGUMENTS ARE X-HOLE FRACTIo^4Sf T-TEM PEPATU^E>Q-PPESSU«Ef V9-EXCESS

VOLUME, G9-EXCESS GibBS ENEHgV* TIRST ThReE Afte9IN^UT,LAST T*(3 ARE

OUTPUT^INPUT IS IN KELVINS ANO ATM,

DIMENbiQN A (8) »g (8) 3l3),V(8)?G(8)»C(a,a),0<S»8)»(<<3,3)'

lJ(8f8) ,E (8) >Y(8),0(a),X(10)

TYPE '?EAL J.KtNl

OATA (KEY = 1

)

OATA(J( 1,2) =-.0038861 6) » ( J<^1 »3) a-.0 120932) ( J ( 1 0 1 3 0737)

A(J(1 ,5) =-.0131962) , ( J(l ,6)=-.0O997547) , ( J ( 1 ,7) =-.0326) , ( J ( 1 ,8/

=

3-. 045a) » < J (2»'») =-.00'*00910)- , ( J ( 2 , 5 ) »- , 008 1 271 2 ) , ( J ( 2 » 6 ) =-. 0 1 43976 ) C, (J(2,7)=-.003),(J(2,8)=-.Q04). ( J (

3

.4 ) » . 000761 571 0 ) » ( J ( 3 . 5 ) =- . 0 03

033743) , (J{3, 6) =-.02*^014) ,(J(3»/)=0,0),(J(3»8)=0.0>» ( J U, 3) =.0022TT

E50) , (J<4,7)=.0) , (J(4,8)».0> , ( J(S,6) a-.05760<»3) ,( J (4,6 )=-. 0575043 ) , F{J(5,7)=,0),(J(5,8)«0.0)» ( J(6»7) »-,04) ,(J(6,8)=-,05),<J(7,3)=.0)

G , (J(2, 3)=-. 002162)

Data (K{ 1,2) =.06298830) , (K ( i ,3) ».0S9737d> , ( < ( 1 .4 ) =. 1 1 39i.7i ) , ( AK(1,5) = .116009) , (K ( 1 ,6) *.0197290 ) ,<K(1,7)».14), ( < < 1 , 8 ) = . 1 745 ) , a (K (2,4) =,0677703) , ( K ( 2 , 5 ) = . 03^6632 ) ,(K(2,o)», 0529034 ),(K(2,7) = C.02) > (K (2,8) =.03) , (K (3,4) =.0249291 ) , ( K ( 3 , 5 ) »- . 0033821 2 ) , (K (4,5) = .0 0199213) , (K (4,6) =.154365 )»(K(4,7)«.0),(K(4,3)«.0), ( K ( 5 ,6 ) = . 154365

)

—E»(K(5,7) = .0),(K(5,8)».0),('<(6,7)=.15),(K(6,3)».18),(K(7,3)=0.0)

F, (K (2, 3) =.01 452 7 ) ,(>^(3,6)».14 7 19),(X;3, 7 )«0.0),(K(3,3)=0.0)

DATA (S=3.676E-S,4.l58E-8,4.644£-3,5.05lE-3,5.056E-8,3.546E-8, —15.389E-3,3. ;0bE-!3)

0ATA(A=2.755E*5,7.773E-5,1^.I65E*5,22.733 E*5, 2 1 .279E*5, 1 .713E*5 , —lJO.bbO£*^,4tf!,y46t*b)

0 AT A (0=1.,1. 5, 1.67, 1.83, 1.79, 1.03, 1.9 1,2.11)

r Hfc.!5E ARE T Hb ACLN T -^iCl TT F iC T U^^S (FUW HOLEC'JLA>< bHAPEs.diC.) ••**

DATA (Y=35. ,45., 60., 75. ,75. '40. ,90. , 105.

)

UATA(Pl=J.i4i5y) , (Nl=6.Utf!SE»23) , (H«8.J143 1 IF(KEY.EQ.0)GO TO 1 KEY = 0 DO 2 1=1,8

J ( I , I

} =g.o

<(I,I)=0.0

DO 2 M=I,a

J('<,I)=J(I,M)

2 K(M,I)=i<(I,M)

1 CONTINUE

-'='J*.i(JlJiib IW = 8 00 10 1=1, IW 10 E (I)=0<I)

00 15 1=1, IW IS B(I)=(2./3.)»P1 *N1*S(I)**3

L)0 dO i = l»lW

DO 20 M=i,iw

D(I,M) =(((a(I)*»( 1./3. ) 3<M> * ( l./S,))/ 2. )*(1.-J( I,M)^ ) )

20 C**! , M ) = ( 1. - K( I, H ) ) ^ ( Ad)* A(u ) ) ( 1. / 2. ) *

1( 0( I» M ) **2 / ( 3(1) * 3(M) ) ) ( 1./2. ) 37
A2=0 S S2=0

E2=0 $ y/2=0

DO 25 I=ltlW

V2=V2*X(I)*Y(I)

DO 25 M=lt IW E2=E2*X(I)»x<M)*<E(I)*e(M) )/2.

A2 = A2 X<I) » X(M) » C( I» H ) • 25 B2=B2*X(I)»X(M)«0<I»M)

V6=V2 DO 30 I = ! IW —A3 = Ad)

gr^-eTT)

E3 = Ed)

V2 = Yd)

VI = FIND VI ( A3t B3* E3* R« V2t Wt T)

Gl = FIND Gl( A3* B3» E3» Rt V2, T)

Vd) = VI 30 Gd) = Gl

A3 = A2

B3=B2

E3=E2

V2=V6

V1=FIND VI (A3»B3»E3»R»V2.P»T)

bi=»-lNU Gl (A3»H3.h3»R,Vii»H»r)

V7=V1

G7=GI

EXCEAS VOLUME AND GIBS ENERGY

G9=0

00 3!3 i = i,iw

V9=V9-Xd)»V(I)

35 69=69-Xd)»G(I)

W9 = -V9

H9 = -G9

V9=V9»V7

G9=Gy*G7

VIWW=V ( IWW)

RTTURTl

END

FUNCTION FIND VI ( A3» 83» £3»R» V2» P» T ) A2 IS THE CONSTANT A* B2 IS THE CONSTANT B* E3 IS THE AC-NTfflCI TY FACTOR.

INDEX = 0 ~~~

1 VI = V2

XI = 83 / ( ^, » VI ) ~

F2 = (( I. * XI Xl^»2) / ( I. - Xl)»*3) » E3 -A3 / < VI > * T)

1- (P » VI) / ( R«T) ~~~~

F3 = A3 / (R»T»V1»*2) - P/ (R»T)

F3 = F3 - ((( XI 2.» Xl»*2) * ( 1 - Xi) 3» ( 1. XI Xl»»2)

1* XI) / (( 1. - XI * VI)) * E3

V2 = VI - F2/ F3

' IF( A8S< (V2 - VI) / V2) .LT. .00001 ) GO TO 2 INDEX = INDEX~r~i —

IF< INDEX .LT. 250 ) GO TO 1 FLAG = ABS( (V2 - VI ) / V2 ) 5 F0PMAT(28H0 aBS( (V2 - VD / V2 ) » IFIO.5 ) 2 VI = V2 ~~~~

FIND VI = V2

RETURN ~~~~~~

END

38
FUNCTION FIND Git A3, B3, E3,fi, V2, P, T ) VI = »2 ; : XI = B3 / ( • VI » Gl =ALOGI 1. / ( 1. - XI tl *i3. *X11 / f 1. - XII * 1 3. • X1»»7I

1 / (2. • ( 1. - XI ) Gl = Gl - as / f • 9 • T'^1 » • ( P • V1> / ( P3 • <? • T ) -1.0

1 - flLOG{ VI ) Gi = R T F3 • Gl

FIND Gi = Gl

RETURN

END

-—

FUNCTION EXCESS(P,OD,T,X)

DIMENSION X(10),F(tO)

KR=0

SC TO 1 ENTRY V IDEL

K f=l

1 CCNTINUE

C iLL ZERO(F)

IF(X(1I .LE..000001)SO TO 2 CALL OATH CH<» IFfT.GT. 190. 555)50 TO 12

PM=VPN<T1 .0 0101

OELP=P-PM

0=SATIT»1)

CALL OPOO(DP,0,T1

D FL0=OELP/nP

0=0ELO+0

F (l) = X{l)*100O./O

GO TO 2 12 D=FINtJ HCP»T,00)

I (fO.LE.O. 0)3=1000.

F (i)=xti)»ioijo./a

2 IF(XC2».LE. .OOOOODGO TO 3 F(2)=X(2)*10aD./5AT(T.2>

3 IF(X(3) .L^.. OOOOODGO TO <* F{3) = X(3)*1(J0 0./SAT<T.3)

W IF{X{t»l .LE..00a01)GO TO 5 F(%»=X<U)»100 0./SATIT,4)

5 IF{X(5I .LE..OOOQ1)GO TO 6

F(5)=X(5)*1C00./SAT(T,5)

6 IF(X(6) .LE..00001)GO TO 3 CALL DATA M2

IF(T.GT.126.6 )G0 TO 7

PM=vPHf T» *.Qaoaoi

OELP=P-PN

0=SAT(T,6I

CALL OPCOfOP, C,T)

F <6) = X(6) *100!)./IO»OELP/OP»

GO TO 3 7 0=FINO l*(P.T,00»

I F(O.L£. 0.0) 0=1000.

F «6) = X ( 6»*100 O./O

3 v=ifloa./oo

V fsQ

DC 21 1=1,6

?1 VS=VS*FfT>

EXCESS=V-VS

TF(KP-GT.0)exCE5S=VS

CALL DATA CH<» P {TURN

ENO

39
00*^*10 N/ OAT a /G, = ,GAM>1 A ,VD, ITP

7

G a "t'-ia-- G { 1) =

1'^ ^g) — —

" G ( ? ) - G ( ) = -C.?UT901^213^1'*1''E Ql

fri—^ ) =^ G( 5) = — . 13 D ru^*? T7Gu;^0C 12

-0.'+22''7!*30 9«t6ol'^7E 0'+ G ( 6 ) - G( 7)-

T.l"OJ?'^60QgU6'4g'*°!"03 —

- -i^. 112 5'9''a2S5?-'a81S-Ql

^ ( ^ ) - G( 9) =

i.t>giS?'?7??g''g9G7^''C'* —

J.I ?4oqil5G160ar.-7c

G ( 1 1 ) - G(ll>=

0.'jlil'tC!0Og5O0?7rjL"07

:.23-?fll6'*5Q3?'?n6£-02

1? ; 12)-

G ( 1 3 ) =

"1 .3'^?75Z^ 'i^''5'yj^*^^. '^3 ^

G .!*'^5j27'33197121(*E-0!t

G ( r 5 ) = -C.^T7if302735£*':575'=: CO

G t i ^ > -

G ( 1 7 ) = —g .7?i7?>'^u j j??('°C£"'!''* ^ -0 . 11161U119 537U2UE-G5

G ( I j ) -

G ( 1 9 ) = -a.2 !?13176 91T2.772 9E-n5

G ( ? 1 ) = .119^1 92i*0 3u:*192P Oo

G ( ^ -

G(23)

n . 55'*63Q7131 = 1 '?23P G5

G ( u ) -

G(Z3)= -C.25633292&a77'i=?Ut Ql

G(?^)= -0.25ri2i*5i+157nj2<^?E CIO G ( 2 1 > -

G (?'5) = a.ia355fe535.8J*;i55P-0't

G ( T ; ) - G(31>= -a . 75-^!tl'5ifl28'a59f5F-o

q f * ; 1 ^

1) =<= lll?192j9i* S 7P <2 )=6 .'*32<=)o75"'9?-l

'/^ ( 1 > V => ( =^ ) = 1 .3i:37-;g9i5r-l •» VP(ti>-7. U'-;29'U93m2g-l

5 « \/P('=.} = .i23 3 VP(7)=6'.15 S 70 ( 9 ) =126 . 2«^ V^t J) U«

40
^ M w V / CM

^i-^; /3 , 3 .3iM"A ,V°, ITS

- < ! ' g !

^ "

-

G ( 5-t—! 1 - - . i gg; i •'rg r^l 9E» : 2

G ( 6^ =

( 3 ) =

T-f— ) -

C- ( 1 ] 1 = 3;ii>-

'r.2) =

G( 1

=

-.l"-5-7r"!7--5'?E-"3

3(15)=

G ( L 7 .' -

. '(1=1= -.l-?-:5213"-'»-2?-Cl

1 : ?l - .i^iT'Sv-i^i;*""';

G ( ? 2 ) = . l = 52^'!l^--^:i£^-:3

3 ( 2^)= .-"2:5ii^c?iiE'*::

.12=5 = 155:?i22£-:2

3 t """I -

?) =

2ii'' = "';';7ggi3-*? .

f 2

" 1 =

3 ( ^: ) =

J ^ - i —

G t " ^ ) = . ''2T''5?5 15^*75;-:!.

'.'? ( ?1 -1

;=(-)-. 11^3??"

V ' ' = ) = 1

- ^-t^:,-: T'J-'.-j-j, 1 1

1 -111 :°:2 (==,21,:'»

41
^2 rrt j ^

—DIMFNSinN Xf3?)

I

'

-' gri S ! n—; 1

3

" 7 . • 1 3 g 7 —EQMivaL e:hc=^ (?,x)

ga r a/ 'o, •'.,3A w na

frr-n 0-^0 —r-rr- — = j * ^ —'jusn^fn '

-

ft --:'; »[]

1^' = ?T ^ 3

' :i ; = —?i " = ^11 ^ 0 —t ; =

'; i:=' t id

- -r» -r —' i, = r j" I

f = =:yp g

s

T P 1 1 ^.

-rr"t

r^ O TG 1

C JMT^r.' U

"

t r) = T ; * "!

7 1 3 ) =,1

2

n( >t > -g > /'

( ^ ) =T

— ) -iO,;/---

( 1 1) =0 —c "

( 1 T) =05

' (15) =36/72

3 ( 17J =oq/'

^ t 1 n - V^ ? - ( 1 9) =n 0/ '

2

"

f ? ;> r^ ;

~

( 27)=n5*- /'^ —(2U)-!i7'f/rg

42
-(25)

B (27) sOa^c/Ti*

= ( 1 1

)

P = P

1-0 TO 1

'!!'i '; ' iu '

_ . U J I ^?2'=5. 0 +-F1*D5

: ( t i -?.:"^?*T

( 2 -f—

t

I—

= 2 . 2''*':-*''S

. a

: 'D2 *T -3.:g '> g2—

= 3. 3 J »n2/T

=? .:

:

- J . I 2 "C *•

= 6 . J ] »:)5/T

9 (

= (

:

T-rt

! 12

( 1 u

- Cr

" ( l"* E (1^

1(11 — r . L - = P 21/ "2

" ( C! 1 i : t 22'

1 -'^ ^1/ ~7

- (2--f

C { 2ol

1 _r TIT / •'•7 -C2tt/'r2

1 -y gU/TH

= ="25/ ~2

* ( ;qi

E ( ?a =P25/T2

( 31 '/- '

43
n — 1—T~: 1 T = l,Tg —

=."i-rrT^T —

p o

^ :

^

ES/LTTPR

CT'iFUSI it "^,6)

r)aT4((a(r),I=l,7)=19n.= 55, 10.15,19.65^12322,6.712 03 0 7 37,

I'-.q^/g: iq/ ;g, ? . % g .e )

^a-^a < f i (1 1 , 1= 9, -30 5. ?3,

:a^3((fl(i) ,i=i5,2i»=35q.fl2

<^-'g»!t3''i;,-i?.?g'.sig6e,ii.J7''i99';i;.g.Q}

,5.,3.6 8i,'+5 8571,iq.0««0 8 571J»,-29.^62613 56

.16 ,'.a2.

211.o021iq ^2, J .0 ) ?.2S^':*i3 5e^.ll.963?7B5q, -1 9 . 9 7? 91 Qqg ,

"iTA ( fa til , -JiO*^

1 ,3.% ^ 7.657 5 35i*0 0,9.1«t52'^12'i3,-l T.10 53 2'.62,

paTa((a(i),i='5,!t2)=i25 .2, 11.21 , 19. 3921 6^^35,26. 01 1*0 81^6 2,-39. '97'^ 8

7

•^F(T.GT.a(l,I )) SO TO 1 saT=(a(2,T)*a (3,i)»x»»( .35 )4-a(i*,r)»x*ar5,i)»x»»('»./3.)

1 1\J -\ t^^

g'n ^

CO-I^O^'/OaTi/G.^.GaMMa.UP.DTP

y=(l.-V?C)/T)/( 1.-7 0(7) / VP fg))

7 r" -1 = '7 ^ I T I - ' I 7 :-' I » J " Ji + V I i J ' ' ' ? J I i J 1 (1 . -XI 'VSfC) ) g"ijg>j

1 y-\'=.::i

- n

S

'J-'-^.JU i IN-. -

' c'^iJ ) —" ' J 1 := 1,

1 y ( ' ) = G .

:

" M-n

44
Appendix D. Program Listing for the Revised Klosek and McKinley xModel

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

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

ways. First using the equation

^^mix = ^ ^i^i - ^\ ^ ^^2 - ^1^ X^^ (C-1)

The V^, and k2 may be obtained from tables 1, 2 and 3 and the volume of

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

C^S.^ + 0. 0487 C^Hg + 0. 0242 nC^H^Q + 0.0241 iC^H^Q + 0 . 0425 and a temperature of 105 kelvin.

The Z X^V^ is obtained from table 1.

E X^V^ = ( . 8130) ( . 037112) + (. 0475) (. 047266) -r (. 0487) (. 061766)

+ ( . 0242) ( . 076100) + (. 0241) (. 077538) + (. 0425) (. 042560)

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

+ (.0242) (58.1243) + (, 0241) (58 . 1243) + (. 0425) ( 28 . 0134) = 20.6168 the molecular weight of the mixture

from table 2 k^ = .730 x lO""^ from table 3 k2 = .849 x lO"-^ plugging all this into equation (C-1) gives

V . = .040944 mix

1/V . = p . = 24.858 moles/liter mix mix '

This compares to the experimental values of 24.850 (see last page of

Appendix E) to within 0.03%.

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

following way

D = FMKM(T,X)

1^ where T is temperature in kelvins and X is a matrix of mole fractions of the

jl; components in the following order:

45
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

for the example: T = 105., X{1) = .8130, X(2) = .0475, X(3) = .0487,

X(4) = .0242, X(5) = .0241 and X(6) = .04256.

46
r» sj- >£ as ^ <r (? -? — O o n IT! «5 (MOO

-y tr o o> o r> >y ^0 LTI o M Lfl P*' o flC (M in

tVI -J- o r> IT ^- — a> o (M ^ vO rr CO O fVI ^ o — 0 !»

CT>^ CT" (?> a o o o o — (V M (\J n -T <r -J' in in mm s e 00 C c> <?> IT ^ ^ IT (J> <T o O 9 o O o o o o o o o o o o o o o o o o o o e o o o o o o

n^scnio ^niM. m (V, n -r \ri 9 r', r*- —ir^ tj> eof^^ ib o

O' 00000 --«-«-"-"(V(MM(\i(Mon r". (n-f^-r^y^ininLP

000 O! 00000 oiooooooiooooooioooo 00000

m 1^ o ^ f- <c^- (soarn — — fu o>in-?'a> p»in in « mm 00 mnr- mo ^ <c- m m' m o (V,

ffl ffi o

<n 1^ 0000

o>c(^J(Vo^cf^'*^op^ae"f*c^co-c^ooi<^X"«CT' iEcT>»TOffi fflm^^»MOC^ofy^c-"tB^-^o^-omf\J(M^>*ff'CT>f^J —-CC'-".'^ 0>o»"fMrt'^mvO^Cofvji>y.a(>.«,rr»o(*^f*fVi p~(\j(B>o-* m^>T,y>r^>T^-T>ymmmmmo^-OP«>f^f^3 cc^oot^ O 00 000 0 00 000 0 O O O O 0.0 00 O OOO •MM

I

I -j>*--c^of»-nor^vcm>oxo.yij"m(M»»o-"(^''Oo-ofvj oo—Ovo I^«•^cmm>».^'^J•nr)nr(n,^^^m^c^-aco^ Oi— o>f>c 33 a <\i -r >o o(\j-*vOiBOfM-»^ffloru.T-as30(\i-y>0!ronmr»o — rivoixofvj sC>CvCvOi.aN''»-r«-^-.r*iBcciB*!Xi7'0(?»^a*ooiOoO'— — rjrvj oooooooooooooooooooooooooo 00000

o

•a a — m

o

X o

-f -T m

r» fw 000

m -r m'm

010

— a m m o o

I o o

o —

<

r»- r- o o

-#^mf»o-Tffv-»-«x»»>of^xo^x *oxr*f» x^vcmm-y'^p^c^(M(\!f\i'M(M<^'^!^ >TmmvOP» nm'*o-"f^m^•c^ — nm'~'i?— f^m f»iT-"'nm

>0>o-c-or*-f»f^f*r-xxxffl'Xi?c?'i> ^(Tooo

0 00000 00 o o o o 0000 0 000 00 ... ^ ............. .1

.

•"<v-*-f^'»-m««^mr^(vi(v;-T'0^ -*(?| -r om <s: ecu ^0f^o^-m^^JO^•mn — (3>f>-m«f\jO(Txr-vami^>TPn«iM(M(Vi(M<^ .*'ax^-MnmvOXO(Mrrm'^(7'-"n-j'sOxo(\iJ-T.oxoru>r'Oxo oooo»"— •— — — Ow(Vfvri.f\.f\,r'r?r"(^r^^,j^^j-mmmirm'£

00000 O'OOi 00000000 eooeoo.ooeo 00000

o(\.^ C'X 0'(\j^vCxo'\j^>cxo{v>»vCxo(Mi,f^x o rj-T«cxo

47
01 o ^ rvj H o (VI in

«• • < • • <M (V fVI (TJ

n in ^» («» o> o m ,r in oQ ^ cc o r? «^

<i)«r< — .roy£iLnr^(Vif\j

MM^vOOHinyaoaO

intni.oxi-.^^n,£)n

<C!<>Of\jrlLni^O«M

-•critnn(M(*i^uvo^

M cj> o — rr >»• >j- in vc r-

• • • « • 4

(M vOl o -J- (\j n CI'

" X nJ o ON o o >' n jl in m ^»

IT >c r- 03 01 © n tr f»- oooooooooo

> I i I I I I I I •

otnoinouloiroin

ono

O

o

so

u

V

U'ou

A<g H

^ f^i••••••«.,, in r-. o m IS. O' a^ t^. i

i^ini»-(\in'rnr"i^^i^

(^4•J•^CIC^(^J^o -.?L^?S

«^<^ — af«~tnf\jain (\ifnin(cD.H^ •••••••••» uuinrvjo

"^^"^""fVitM Mfn.y!in

I

, I

J i i

' acvjotnaa— vflp^f^^

m o in o (M r» o <Mi ^ r»< o ini (VI

i (VI (\j (M ni ,f

vOinf^f^fviLn oir)(Vi,(3s Dio«nini>o n.t^rn

i

' ! !Ei^aci<j»rMLn X!Xoi»-

•I • •! • M s • „ ,

I «|-, fVj f,,! ^ III;

o^c«<Tiin(\joLnr)a:io

v£i<roNe(vj(n(n(vj£i,ji

I H «- <\l (VI m

«-» (VJi

^ 1 oo^•nl^(Viln ' LT (\i in mfn(noo (^ lAin «•••••««, vo. f"" 01 ». ^. (VI vo

j j — — CVl M

ir(m^«MMtn 03 fi^ o

(Vii CO <ti (VI o^l(VJ —1 n .01 o (\j (VI m ini > — •j' a

I — — (VI aMvo,f(viirirc^ir

-•-«».(Vj(^in ^ cnh.

S3o-"-^(VimvtLrr^ ooooooocoe

I I I

3 airoincJir oirom oi o ru ^

48
FUNCTION FMKM(T»X)

DIMENSION TM(150) TN(150) X(IO) ,0(8)

UAI A 19,72 15139)

( rM( n ,I = l,15)a-.005».A2,.22,.34,,43».51 1.59».66*.75,.82,

93, .98,1. 03, 1.08)

DATA

A.as,

DATA

A, 99*

( IM( I) ,1=16, 30)=-. 006», 14,. 26,, 38,.49,. 38 ,,67,. 75,. 95,. 92,

.05*1.1,1.15,1.2)

DATA

Al.ll

(TMd) ,I=31,45>»-.00/».lb,.3,.42,.54,.65,.7$,.86,.95,l.d4,

1,17,1.23,1.28,1.34)

<TM(I) , 1=46, 60 ) =-.007,, 17,. 34,. 46,. 62 ». 73,. 84,. 96, 1.08, 1.16.

1.31,1.37,1.43,1.49)

DATA

Al.24

(TM(I) ,1=61, 75)=-. OOa .I 9,. 38,. 54,. 7,. 82*. 93* I. 06, 1.21, I. 3,

1.47*1.53,1.6,1.67)

DATA

A1.39

DATA

A1.56

(TM(i) ,l=76,yo>=-.00y*,2«i*.42,.61,«7y*.93,l.06,1.2,i.36,1.47,

1.65,1.71,1.79,1.86)

<TM(i) ,1=91 ,105) =-.01*. 25,. b*. 7,. 9* 1.04,1. 23*1. 4,1. 34,1. 65,

1.85*1. 92, 2. ,2. 08)

DATA

A1.75

DATA

11.86

( I Md), 1 = 106, 120) =-.013,. 3,. 59,.79, 1.02, 1.18 ,1.38, 1.6,1.73,

A1.97

DATA

2.08,2. lb, 2. 24,2. 3J)

(TM(I) ,1=12 1,135) =-.01 5,. 35*. 7,. 92* 1.14, 1.36* 1.6* 1.73, 1.96,

2.22*2.34,2.42,2.52,2.62)

(TM(I) ,1=136*150)=-. 017*. 4*. 80, 1.06, 1.39* 1.51, 1.77, 1,9,2. 23*

2

A2.09

DATA

A. 38*

DATA

Al .rj3

DATA

.52,2.64*2.74,2.85*2.95)

(TNd) *I = l*l5)=-.004*.l*.22».35*.5*.6*,69*.7a*.86*,95,

1.12*1.20*i.2/*l..i5 > (TN(I) ,1=16, 30) =-,005,* 12 ,,28*, 43*. 59*, 71*. 83,. 94, I. 05 , 1.14*

1.28*1. 3/, 1. 45*1. b4»

(TNd) * 1=31*45) =-.007*, 16*. 34*. 49*. 64*. 79*. 94* 1.08* 1.1 7, I. 27,

A1.22

DATA

41.37

DATA

1.4('*1.5/»1.67*1. //)

(TNd) 1=46*60) =-.01*. 24*. 42*. 61 *.75*.91* 1.05* 1.19, 1.33, 1.45,

Al.'bH

DATA

1. 6^*1.81*1.92, 2. OJJ (TNd) ,1=61 ,75) =-.015*. 32*. 59*. 77*. 92, 1.07 I.22* 1.37* 1.52*

TITTT

A1.83

DATA

A2.17

1.97*2 .1*2.23 *2.36 ) (TNd) I ^790 ) =- . 024*, 55,. 72*. 95* I. 15*1 . 22*1.3*1.45*1,6572 . * 2.32*2.47*2.63,2.79)

DATA

12.45

(INd) ,1=91, 105 >=-.0J2,./'5,. 91, I. 23*1. 43*1. 63* 1.85*2.08,2.3*

A72T5

DATA

2.77*2.95*3. 13*3. 3?1

(TNd) ,1 = 1 06* 120) =-.043*1.* 1.1 3* 1.48 I. 73 I. 98 ,2. 23* 2. 48, 2. 75

A2.9*

DATA

A3. 32

.1.3.3*3.52*3.74*3.96)

( INd) * 1 = 121 * 13b )=-.Obfl*l. 34* 1.46*1.^2*2. 2*2. 42 ,2, 63* 3.,

3.52*3.71 ,3.95,4.2*4.46*4.74)

A3. 99

(TNd) *I^''3«TrSTJ )=-.0/5*1.7^*2.*2.4*2.6*3..3.4*3.77,

4.23,4.47,4,76*5.05*5.36*5.69)

1) .LT..00001)GO TO"^

01=1,8

X(I)»Q(I)

OtAL(T*x)

"TFTT —AW=0

UU~1

1 AW= AW VI=V

J=l

IF(T Ge.95.) J=16

IF(T

IF(T

GE.IOO.) J=31

GE.105.) J=46

IF(T

IF(T

GE.llO.) J=61

GE.115.) J=76

IF(T

IF(T

GE.120.) J=91

GE.125.) J=106

49
IF(T.Ge.l30.) J=121

JJ=J->1» w= i b • UU b i— Jf JJ

1 — W 1 • IF(AW.GT.»*)GO TO 5

3 CONT INUE

T — 1 1 i — J J

6 DIF1=AW-W

J=I-1

FK=(TM( I)-TM( J) )»0IF1*TM(I)

FKl=(TM<I*15)-TM<J-»15) )*OIFl

IT=(T*.00001>/5.

TM(I*15)

0IF*2=T-IT*S

1F(T.GE.135.)OIF2=T-130.

IF(T.LT.90.) DIF2ST-90.

FK=FK* (FKl-FK) »0IF2/5,

IF(X (6) .LT..0001)GO To 17

FKN=(TN(I)-TM( J) )*DIFl*TN( I) FKl=<TN( I*15)-TN( J»15) )*OIFl TN( 1*15)

FKN=FKN* (FKl-FKN)*0IF2/5.

17

FK=FK*(FKN-FK>*X(6)/,0425

FK=FK/1000.

FMKM=1 ./ ( VI-FK»X ( 1 )

)

RETURN

20 FMKM=0.0

RETURN

END

FUNCTION V IDEAL (T»X)

DIMENSION X(10)

V = 0 J=0

IF(X (5) .GT..0001.AND.T,GT.il5.) J»l

DO 10 I=lta

IF<X<I) .LE,.000001)GO TO 10

IF( J.GT.0.AND.I.EQ.6)GO TO 10

V=V*X< I)/SAT(T,I)

10 CONTINUE

IF( J.EQ.l) V=V*X (6)/SATN2(T)

VIDE A L = V RETURN

END —FTJNrrTUNTSFP^STn —UtL!

IF(T.LT.115.)G0

= H-ilb.)

TOl ^

SATN2=SAT(115»t6) PELT* (SAT (115.05*6) -SAT (114. 95«6) —RETDW^J ~

1 SATN2=SAT (T*6) —RETURN

ENO

50
FUNCTION 5AT(T,I) ~

UNITS < AND ^OLES/LITER

DIMENSION A(7.8)

DATA ( < A (I ) . 1 = 1 ?) =190 .555 < iQ . 16. 1 8 . 658 1 2322 , 6 . 7 1 203 0737 > 1-. 9^72019702, 0.0. 0.0)

DATA((A(I).I=6fI-*)=305.33.

1 6. 36, 12.55205121 . 1 3 . -'328^373 1 9 . 0 0 '6 1 066 , 1 1 . 37715935, 0.0)

DATA((A(I),I=15.21)=369.32,5..a.68^45867l,13.0^0a571^.-29.:*6261356

If 16. -355911a, 0.0)

DATA( (A(I) ,I = 22,23)«^25.16,3.92,

1 7.2860 62567, 1 1 . 96307 859 , - 1 9 . 3 759 1 962

,

211.6021 1932,0.0)

DATA( IA(I) ,1=29, 35) =408. 13, 3. 3,

_1 7 .657535'*0 0 ,3. U52512Q3.-13. 13 532^6 2,

23.145894091 ,0.0)

DATA ( 1 A (I ) , 1 = 36,42) al 26.2, 1 1 . 2 1 , 1 9 . 392 1 68 35 , 26 . 0 1 40 8462 , -39 . 497587

191,23.32977312,0.0)

DA~A ( (A ( I) , 1=43,49) =469. 6, 3. 285, -.03620 04993, 59. 0 02 02990,

1 -93. 193 8 19, 43. 66 78 0333, 0.0)

DATA( (A(I) ,1=50,56) =460 .39,3.271 , 2 . 9463 1 0 '*56 , 35 . 5077097 9 , 1 -57. -» 12^2993, 23. 15898 339,0.0)

I" (T.GT . A ( 1 , I) ) GO TO 1 X= ( 1 .-T/A ( 1,1))

5AT=(A(2,I)*a(3,I)^>X**(.35)*A(4,I)*x*A(5,I) X** (4./3. ) l*&{6,I)»X«-9{5./3.) ) ^s"TUkN

1 SaT = 1. E*2a

=?ETUSN End

51
Appendix E. Program Listing for the Cell Model

iUb KUU 1 XNt rU KNQPI (PiNtuUUI* i IN»QI

nwin* c.UN':.*'! -rtriuiN ucni^i T nuuri. tl_ wrWb nu LNGO

1 M ^ n THIS PPOGRfln IS OESIGNED ^Ok THE CALCULATIOM OF LNGO

1t-''" UK 1L TniiTn lU Ul U nPN^TTTP*; 'Jt:ri:b 1 1 Ita tmi LI>ILTv AMU amo uti HILLi wot NUI L NvjU

COMPUTE ENSITIES ABOVE 160 K« LNGO

LNGO

LNGO

L NIjU

"EA5URcO BY LNGO

1 Mftn L riWU NATIONAL BUREAU OF STANDARDS LNGO

1i_ Mfin nuu BOULOER» COLORADO LNGO

1LN&U Mr H LNGO

LNGO

COMPONENT ID NUMBERS APE LNGO

41 MCft- TU1 n AA MCN!r 2 ETHANE

J PKUPONt

6 NITkIGEN

LNGD

LNGO

PIN=PRESSURE IN ATMOSPHERES

TINS T'^MPPP fl Tl IB F TN nFf^PFP"? i^FI \;TN

ij^nftlRiX Or MOLE p'^flCTIONS Or CunPONENTS

OUTPUT VARTtqLF IS

0OUT=OENSITY IN MOLES/LITE"

OI'IENSIQN VHOL0(12» , 7PH0LD < 1 2 J , Q ( 6)

COMMON /PUN/ID (12), X (12) , NAM ( 2 , 1 2) , C 1 2 ( 12 , 1 2) ,R(12) ,Z(12) ,S(12> .VSLNGO

1(12),TS(12».US{12S.SG(12),E5>(12» .LAM{12) ,NC,MW(12), AIJ(12,12) ,P5T(LN(;o

212) ,TCT (12) LNGO

COMMON /0AT/T9T (12) .7RT (12) ,TPTM(12) . V8TM (1?) ,C (12) .SGTM(12)

,

STMdLNGD

12) ,EPIM(12),PIM(12) ,STN(12) ,VSIM(12) , USIM (1 2 ) , TSIM( 12 ) , OV 91 M ( 12 ) ,PLNGO

20(12) ,PV(12) »PHO( 12) , VBTMP(12).TTM(12) ,MWM,CNT1,CNT2. TOLD (12) .INCRLNGO

3(12) ,SMrTCH, JPCJPCS, JMlXtOENS, VEX, HEX ,GEX, TMP, VHP, TP LNGO

COMMON/PAR/KIJ ( 3, &»,AJI( 6, ) LNGD

COMMON/ UNI TS/TTC, IPC , T , TMAX, OT, P , PM AX , OP , PS LNGO

TYPE REAL MW,LAM,MWM,INCR,iriJ,M0L,LAM8

TYPE INTEGER CNTl , CN T2 , SWITCH, CODE

PsPIN

T = TIN

1 CALL 7ER01

C /LL IN°UT(Q)

I F(T.GT . ( 160. ) ) SO TO 19 LNGO

3 CALL PZERO(CTMX» LNGO

HWM = 3 LNGO

00 q I = i,NC LNGO

"WM = MWM 4- (XCD'MWd)) LNGD

<3 CONTINUE LNGO

52
Jij ij^ J. .- J. tm^, . _ TCT#T* _ T / T^#T4 TtlClJ - I / T5(ll

1. r,uu LNGO

tiniltMCfTQTfTk \l Q T t T \ 10MD KIP% L NUU

TdlMtl) = T / TSIMtll LNGO

11 C ONT INUc LNGO

V r1 — U • U L Nlj u 00 12 I = NC LNGO

1

2

U J N 1 i NU C L flu U

U INo u DO 13 I = ItNC L NbU

1 Mr n

V r HOLD I If = VDirHlJ LNGO

1 M(t n Vol nr fli = VoXtXI L NGO

C Pt i CO f OO V/DTMOfTl TPT/T^ MP 1 \iOT#T* -» tfBTUOfT\ VcICil = vdI^P^I) LNIjU

PO — fO » TCTMf T1 1 / (I^TM*TI

VDlnPfl) = VTlrlTlJ LNGO

pail DOC^ f OO URTMOfTl -TQTMITI MP> f wen

vBInll) = VBInP(I) LNGO

P PM TTiai IC VMP = 0.0 LNGO

n f 4 ». T — 4 MP

Vio = VP * ( If 1 IJ •ValnP ( I »*vSIn 1 1 J J L NGO

PO(I) = VOI^-Pd) • VSIM<I» LNGO

l** C ONT INUt 1 M r* n npMC _ ^ T J *— MUf4/WMO o w f~ / V n

" nniiT— ncMC*i nnn /mum

1 7 'J u u 1 — y • u RETURN

CU"nijN /'^UN/a tool J T t 3

UVJ X X XV'^OX

1 ZERO

UU ^ X — XtC&M

2 ZERO

O CT! ID U 7 c n ZERO

SU^ROtJTIME VOLUME (TfV»J»MC) VOL

V UL

I f (TR«GT» ( l.OOl ) GO TO VOL

V - c.5 . 111/ niUU

1 VT ~ (l.OJ ( 0 .1 'T^'V** (t»,0 ») 10L

'•rr — ll.J) ~ IVfVil

TEST = aBS(c'?I?» VOL

V UL

V = VT VOL

rbUn TO 4

( U 1

>jni V UL

2 7 = V**(^.0) VOL

i 9FTURN VOL

I* V = (( C (( (10.06600 •TR>-2'».79a37)»TR» 23.260722)»T!?)-6,6a6880» VOL

GO TO 3 VOL

END VOL

53
SUBROUTINE INPUT(Q)

u i ' i v^'i cjf.jj.wn, oF«i-Mno» o # » nc. , t • Of.o

1L( 5),CT( 61,TCH( 6),VCH( 6),eCHt 6 ) , AR ( 6»,/SZt 6>,QI6)

!1U \ COMMON /f?UN/ID(12).X (l?),NftM (?.!?». ri?fl?.1 .P(12» ,7(1?^ ,_S (12) , VSTN

1(12) ,TS 1 12» ,US (12) t SG(12» ,EPa2) , LAM (12) , NC t MH ( 12) , AIJ ( 1

2

,12) ,PST(IN

212) ,TCT ri2) IN COMMON /O AT/TBI (12) , VBI (12) ,T3IH(12 ) , V8IM(12) C(12) « SGIM( 12) , SIM ( UN

12) ,EPTM(12) ,PIM(12) , ST M ( 1 2) , VSTM ( 1?) . USTM (i 2) . TST M{ 12 ) . OV M ( 1 ? ) .PTN

20(12) ,PV( 12) t RH0(12) , VBIMP ( 1 2) t TTM ( 1 2 ) tMH M, CNTl , CriT2, TOLD (12) , INCRIN

3(12) .SWITCH, JPC.JPCS . JMTy.OfiNS. \/FX. HEX.GEV. TMP. UMP. TP TN COMMON/PftR/KIJC 6» 6),AJI( 6, 8) IN TYPE PEAL MW, LAH.MHM, INC. KTJ, MOL, LAMB

TYPE INTEGER CNTi , CNT2 , SWITCH

OATA STGM/ IN •C.<39iaOQ,l.C2qOOO 155 0 0 0,1. 27 3 0 00, 1.38875 2*1.392995/ IN

DATA EPSI/ IN

»0.6'*0 000,0.90 9000,1.698 00,2.237 0 0 0,2.705262,2.5'»5907/ IN

OATA LAMB/ IN

• 1.0 53601*, 0.98 6325, 1.2 27 117, l.ifO 8519, l.i» 73 3!t6,l.i»61675/ IN OATA MCL/ TN

*2 9. 0160 0, 16.0*»200 ,30 .06d0'3,4i.,0 9'»00,5 8. 12 000,53.12000/ IN DATA SNO/ IN *ia. 30000, 10. 000 00. 10. 00000, 10. 000 00, 10. 00 000, 10. 0 00 00/ IN OATA CT/ IN •126.0 60 0, 190. 56 00 , 30 5. 'SO 0,369. 8 200, '25. 160 0 , i»0 8- 030 0 / IN

OATA TCH/ IN

•1 12. 7699, 170. geJ^S, 25 6. 3 3 11, 2 9'*. 7255, 32*0 . 7 ?67 , 322 . 61 0 9/ IN OATA 7CH/ TN

»26. Cia*»6, 29.0 '010 ,'0 . 881 3 8, 5U .6 0 301 , 6 fl. 72075 , 69.'^«^272/ IN OATA ECH/ IN •1393.0 0 3, 1977.0 00 ,3695. 0 0 0, '867. 0 0 0, 5 886. 652, 5539. 395/ IN OATA AR/ IN •1.0 00 00 0,1. 0000 00, 1.0 00000,1.000000, 1.0 00 000, 1.00 00 00/ IN

OATA AZ/ IN

•lO.il 0000, 10. 000 00 , 10. 000 00, 10. 000 00 , 10. 00 000, 10. 00000/ IN

DO'^ 1=2,6

« X (I)=0( I-l)

X (1) = 0( 6)

Nc=a

0 0 1 1= 1 , 6 IF(X( I) .LE.O. 0)GO TO 1 MC = NCH

X(NC)=X (I)

TnfNri=T

1 CONTINUE

00 2 T = l.NC m

J = ID (I) IN R(I) = AR(J) IN Z(I) = aZ(J) IN

S(I» = SNO (J) IN TSTT)= TCH(J) IN

US(I)= ECH(J) IN SGd) = SIGM(J) IN

T rr (T ) = CT( J) IN £3(1) = EOSI(J) IN L4M (I) = LAMB (J) IN VS(I) = VCH(J) IN

54
MW ( H = MOL ( f

)

TN

Z CONTINUE

DO 3 T = l.NC

IN

T N 00 3 J - 1»NC

M = 10 (T)

IN

m

L = TD(J»

C12fI«J) - KIJ(M, L)

IN

IN C12(J,II = !<IJ(LtH>

fllJ(I»J) = flJl(>1»L) ININ

3 AIJ(J,I) = flJKL.M)

CONTINUE

IN

IM RETURN

ENO

IM

IN SUBROUTINE PRES C4 ,B» C ,NC1

TYPE '?EAL H,P»V»T»Kl,<2»K3»VT,PTtK'»

PRES

P = A V = 5 PRES

PRES

T = C

H = . 0 1 PRES

T F(H.GT.P» H = P ASSIGN 3 TO KK

PRES

PRES

1 CALL 9ETA(P,K1,T,V,NC>

Ki = H » <1

PRES

P9ES

VT = \/*Kl/2.

CALL aETACPT,K2,T,7r,NC»

K2 = K2 • H PRES

7T=V-H<2/2.

CALL BETArPT, K3,T,\/T,NC) PRES

<3 = K3 » H PT = P H PRES

PRES

VT = V •• ( K3)

CALL BETA{PT, KU,T,VT,NC)

PRES

PRES

y=VKKl*2.»K2-»-2.»!<3+K«») /6.

PRES

P = P - H TF(O.EQ.(0.01 ) GO TO

PRES

PRES

Ir(B.LT.(O.C> ) GO TO 2 GO TO 1 PRES

POFS

2

3 GO TO « , (3,'») P = P 4 PRES

»RES

H = P ASSIGN TO X<PRES

PRES

W GO TO 1fl = P PRES

PRES

9 = V C = T ORES

PRES

PETURN

ENO

PRES

PRES

55
SUBROUTINE PZEBO<TRT) PZER

COMMON /RUN/I0(12),X <12) ,NAM<2»12),C12C12,12) ,R<12) ,Z tl2) ,S (12) , VSPZER

1( 12» .TS(12» tUSC12) «SG(12) fEP(12) .LAM(12) ,NC»MW(12> tflIJ(12.12> .PSKPZER

212) ,TCT(12) PZER

COMMON /13AT/TBI(12) ,VBI tl2) , TBIMf 12) , V3IM (1?) ,C 112) , SGIMU2) , SIMdPZER

12) ,EPIM(12) ,PIM(12),SIN<12),VSTM(12) ,USIM(12) ,TSIM(12) ,r)VBIM(12) ,PPZER

'^nfJ'^t 0\ff4^k OLJA#4^ft tfOTUn#4^% T7U#-40t %AlJkJ /^ftlT4 ^%t7'9 n/41t 2U(lZi^rvil2»t "HOT 12 » » v9 I nvf IZi TTrifl2) t^Wn* CNTl , CNT2 »TuLu(12> « INCRPZER

3(12) »SWITCH»JPC»JPCS»JMIX»uENS» VEX»HEX»GEx» TMP,VMPtTP PZER

COMMON/PAR/KIJ ( 6» &)»flJl( 6» S) PZER

C CMnUN /UN IT5/IiCtIPC»i»TnAX»Uit'^»PnAX»uP»P5 PZER

TYPE REAL MH ,L AM ,MHM« I Nf^R» KT J» MOL» L AMB

TYPE INTE'jER CNTl » CNT 2 f S witch

IF(NC«Ea.l) TPT = T/TCT(1) PZER

IF(NC«GT«1) CALL TCM(iRT) PZER

IF(NC.GT.l) TRT = T/TRT PZER

iFlNC.EQ.ll CALL PURE i TRT » TRTt R ( 1 ) t RXX) PZER

0 0 1 I = 1»NC PZER

TCxX = T/TCT ( Ii PZER

IF(NC»GT,1) call pure ( TCXX, TRT, R ( I)

,

KTR> PZER

JPC - Q

cr o

I F{TRT. GT . ( .87) ) JPC = 2 PZER

I F ( TwT . GT , ( 1. 0 ) ) JPC = 1 PZER

IF(NC.EQ.l) RTR = RXX PZER

ThtRE ARE SEVERAL OTHER ^uRMS OF THESE EQUATIONS PZER

PE^ER TO ORIGINAL ARTICLES FOR VALUES TO USE PZER

Sli) = RTr • Zlli ~ Z» * yTK * 2» (3 7 C Q

SIMd) = S(I) PZER

r Lc.^ EP ( I ) = US ( I) / S ( I) PZER

ClI) = LAKI) I 21f 6 . / { ( 185 • 6) * ( 1» 98 726) J ) Q T D

TT"^ (T) = TS (I

)

PZER

TOLO(I) = TS(I) PZER

INCR(T) = (25.0) PZER

1 CONTINUE PZER

J CU R = 0 PZER

CNTl = 1 PZER

C ^T2 = 1 PZER

J I X = 0 PZER

2 OEN = 0 PZER

00 3 I = ItNC

0 HN = OEM ( X ( I ) • S I M ( I ) » PZER

5 CONTINUE a T o

t w ^ PIM(I) = (X(I) • SIM(I)) / OEN PZER

k CONTINUE PZER

00 6 I = l.NC "ZER

SGIM(I) = O.Q PZHR

0 0 6 J = l.NC PZER

M = I PZER

N = J "ZER

IFd.GT .J) M - J PZER

IF(I.GT.J) N = r PZER

IFd.EQ.J) GO TO 5 PZER

TRUOX = lAIJtN.M) /<T/TTM{I) )

)

PZER

TF(TPUOX.LT,{-1>10.0I ) GO TO 5 PZER

SGIM(I) = SGIMdJ «-((PIM(J» ((ISG( I)»*(l./3.» SG ( J) C 1. / 3 . ) ) PZER

1/(2.01) **3))» (>IJ(M,N) • EXP (AIJ(N.M)/(T/TTH(I) ) ) ) I PZER

56
GO TO 6 <*7PO

5 SGIM<I) = SGIM(I) *<PIM(J) • ( ( (SG ( I) •(1./3. ) «• SG( J ) *• (1 ./ 3 . » ) PZER

1/(2. CI) ) J r fa L ~ 6 CONTINUE PZER.

"EN ~ Q.O

00 7 I = 1,NC "ZER

DEN = OEN * (PI'^(I)» SGIH(T)» SGIMd)) PZER

7 CONTINUE PZER

00 3 I = 1,NC PZFP

SINdl =«S(H (SGIMtl) (2.) n / OEN PZER

CONTINU E P ZCP

DO 9 I = 1,NC PZER

TEST = - {STM(I) / SIN(I)I PZPR

TEST = 4BS (TEST) PZER

IF ( TEST ,GT . (0 . 000 Ql) ) GO TO 10 PZER

9 CONTINUE PZER

GO TQ 12

10 CO 11 I = 1,NC PZER

'^TV(T) =(STM(TI SIN(T5) /(2.0I B 7F!? 11 CONTINUE PZER

O 1 J J- ~ U I** 1 J. ^ ^ *^ ^crr IF{CNT1 .GT,25 0) 30 TO 12 fZER

G C TO 2 12 0 C l^* I = 1,NC PZER

SIM(T) = SIHi 1) i'ZER EPIM(I) = 0.0 PZER

DO lU J = 1,NC OZC'R

K - I PZER

L = J B7F9

IF(J.LT.I) K = J PZER

I^(J.LT.I) L = T P7FP

IF(I.EQ.J) GO TO 13 PZER

TP'JOX = C12{Lf<> / (T/TTM(T>) PZER

IFtTRUDX.LT. (-130.0) GO TO 13 PZER

EOIKI) = PPTMd) ( (PIM(J) • ''QRT (EP (T 1 'FP ( J) } ) • 1(C12(X,L) • EXP( (C12 (L,K) / ( T/TTM ( I ) ) ) ) )

)

PZER

GO TO !<* PZER

13 EPIM(I) = EPIMd) > (PIM(J) • SQRT(EP(I) • EP(J))> PZER

CONTINU

-

P7FR

ASSUME NUiBER OF MOLS OF FIXTURE =1.0 PZER

VSIMfl) = 9(I» (SGIM(I) ••(3.0)

)

PZER

U5I)H(n = "sTMtTl • coTMfTI P7rp

TSIM(I) = USIM(I) / ((1.98726) • Cd)) PZER

15 ^ONTTNUP P7F!? 00 16 I = 1,NC PZER

TST = (1.0) - (TST M ( T 1 /TTM ( Tl 1 P 7^9

TEST = A8S(TEST) PZER

IF (TEST .GT. (0 .00001) ) GO to 17 'ZER

IS CONTIMUE PZER

RETURN f*ZE R 17 00 20 I = 1,NC PZER

IF(TSIM(I) - TTMd) ) 13«20»19 PZER

13 TNEW = TTM(I) - INCRd) PZER

IF(TNEM.E0.T0LD(r)) INCRd) = INCR( I) / (2.0) PZER

IF(T>fEH.E0.T0La (H ) GO TO 18 PZER

TOLOd) = TTMd) PZER

57
TT^(T) = TMFW PZER

1 q GO TO 23

TNEH = TTM(n TNnR(T)

PZER

PZER

IF(TNeW.£Q.TOLO(I)) INCfl) = INCRd) / TFfTNFW.EO.TOI OfT) ) GO Tn iq

(2.0) 3ZER

PZER

TOLOtI) = TTM(I)

TTKI) = TMEW

PZER

PZER '5 n Zu CQNT INUc

CNT2 = CNT? 1 PZER

PZER

TF(CNT2.GT.25a) RETURN

GO TO 2 PZER

PZER

END PZER

SUBROUTINE PURE(TZ,T,Z .Rl PURE

DIMENSION fl(15)

OAT a a/ .qi9U7flO,-.15 3 06«*7,-. 109 0 050, . 307388 3,1. '1.130 3,

PURE

PURE

1- ;a.a59<»'»,-6. 0'tl587, 51.2 6758,.9 0&250 0,-

2136.1^»06,-U5. 79125,-38.'t3750,2D.56250/

108.9805,23.38672, PURE

PURE

IF(TZ.LT. (. 8653525M R = Z IF(TZ.LT, ( .8653525) ) GO TO 2 PURE

PURE

IF(T.LT. (. 8653525)) P = Z IFfT.LT. (, 8653525) ) GO TO 2 PURE

PURE

IF(T.GT . { 1. C» ) Ta = 1.0

IF(T.LE. (1.0) ) Ta = T PURE

PURE

p = 0.0

TT = tTa - (.9267292)) / ( .7?<i7517E-0 1) PORE

PURE

DO 1 < = 1,11,

P = P + Ado-K)

PURE

PURE

1

R = R TT CONTINUE

PURE

91 IP P

2 R = R * A (1)

RETURN

PURE

PtJRE

E ro PURE

SljnccuTTN^ BFTaCP.riV.T.V.KK) iCTA

DIMENSION C(ll)

DATA AF/0 . 115 6656!»E •0 2 / , 3F/-C. 5 35 10 1 < '£0 1/ , CF/-0 . 7a5932Q 7E- C 1/

,

3 ETA

10F/0.67 36 8653E*00/,EF/-0.11939fl87E*00/,AG/0.52721813E*01/, BE 2gG/0.'«7 693 765E»Q0/,CG/'-Q. 16 0 230 8 OE* 0 1/ , OG/Q . t»98377i,&E» 0 0/

,

3 3EG/-0.'*26 3918 3E-G1/

DATA C/-.113659322E>-0 2,-.55Q9Q99E^-0 0, 'f 1721 0 2E*'0 1 , - . 8 9 966 85 E »q 0 , i-.i500376E<-01 ,-.195 8 32i»EtOa,-.27 8 8988E*01,.5195293E + 0 0,

2. 373t»87SE»01, . 1 36 19 QUE »0 0 , . 'e?! 9<»8E-01/

F = AF OF'V) {CF»V»V) ( OF'V^V* V) ( EF •V*V»V»V I 3ETa

IF(F.LT. (0.0)) GO TO 1 3ETa

Fl = r8F*(CF»7»2. )+(0F»V»V»3. ) > (EF»V»V»V»«». )) 3 1T*EXP(F)

G = AG* (RG»V) +( CG»V»V) (DG»V»V»V» 4-(EG»V»V»V»V) 3ETa

IF(G.LT.(0.0O)) SO TO 1 3£Ta

Gl = (8G*(CG»V»2. )*(CG»V*7»3, «• ( EG »V»V*V»«». ) )> 'EXPtG)

Gl = -Gl 3ETA

DEN = Fl Gl SETA

0V=1./DEN

I f (OV.GT, (0.0 ) .OR.OV.LT . (-1. 0)) GO TO 1 BETA

GC TO 2 aeTA

191= C(l) C(2)»T * C(3)»V SETA

B2 = C(^)*((V»C(5))**(2 ))* EV" ( (C(6) )» ( (T»C(7) )**(2 )))

83 = C(ll) * (V*C(8) )*• (C(9) )/(T»»(C(10)) ) BETA

OV=qt-»-=j2*33 9CTA

OV = EXP< OV) Dv = - gy 3ETa

2 RETURN 3ETA _ E to • 3ETA_

58
SUB^OUTrNE TCn(TMC) TCM

TYPE ^EAL .LAM, MHH, INC^, <IJ, HOL, LAMB, NUH

TYPE INTEGER CNTl , CNT2 , SHJ-'CH aiMENSION 7CI ( 6).TH<12^ TCI

COMHON /RUN/T0(12 ) ,X fl2) , NAM (2, 12 ) ,C12 (12, 12) ,R (12) , Z ( 123 , S { 1 2) ,VSTCM

1(12) ,TS (12 1 ,US(12) t SG (12) ,EP(12) , LAW ( 12) . NC, MW(12) , AIJ(12 ,12 ) , PST tTCH

212),TCT(12) TCM

Cn^HON /0aT/T3I (12) , VBI (12) ^TBIM ( 12 ) , V8 II (1 2 ) , C (12 ) , SGI M (12 ) , SIMdTC-l

12) ,EPIM (12) ,PIM (12) , SIN (12) , VSIW (12'> , USIH(12) ,TSIM{12) , 0i/3I.'< ( 12) ,PTCM

2!) (12) ^P'/< 12) , PHO( 12) , V9IMP(12) , TT'^(12 ) , M, CNTj , CNT2 , T OLD ( 1 2 ) ,INCPTC>^

3(12),SWITCH, JPC,JPCS,JV'IX, OENS, VEX, HEX, GEX,TMP, VHP, TP TCI

COMHOX/PAR/KIJ( &, o),AJl( 6, 5) TCM

C01M0N/UNITS/ ITC, IPC , T , TM AX , DT, P , PH AX , OP , PS TCM

OATA VCI/ 1. 1. 59« 2 .27, 3. 18,^. Q3, 21/ TCM

OC 1 I = 1,NC TCM

J = ID (I) TCM

V = VCI (J)**{2./3.) TCM

TH(I) = X(I) * 7 TC^

1 CONTINUE TCM

TT7 = 0.0 TCM_

00 2 I = 1,NC TCM

TTZ ~ TTZ » TH(I) TCM

2 CONTINUE TCM

00 ? I = l.NC "^CM TH(I) = TH(I) / TTZ TCM

3 CONTINUE TCM

SUMl = G.O TCM

SUM2 = 0.0 TCM

< = NC - 1 TCM

DO q I = 1 ,< , TCM

L = I 1 TCM

DO J = L,NC TOM

TTZ = (TCT(I) -TCT (J) ) / (TCT (I) rCT (J) ) TCM

TTZ= ABS(TTZ) TCM. T12 = t (((({{ TTZ»(-3. 033) ) (5. i»*3) )*TT2) +(-1.3W3) »»TT2) TCM

1 > (C.2 ?7) )*TTZ) - (. 0076) TCM

T12 = T12*(TCT(I) TCT(J)) • (0.?) TCM

SUM2 = SUM2 » ((2.)*TH(T^»TH(J) *T12) TC*

'* CONTINUE TCM

SUMl = SUMl » (TH (I) TCT ( 1) (1. S) ) TCM

5 CONTINUE TCM

T^C = SU"1 » SUM2 * (TH(NC)*TCT ( MQ * ( 1. 9) ) TCM

V = 0.0 TCM

00 6 T = l.NC ICM.

J = 10(1) TCM

TH{ I) = X ( I) * VCK J) TCM

V = V TH(H TCM

^ CONTTNU; TCM

00 7 I = l.NC TCM

TH(I) - TH(I) / 1 TCM

r CONTINUE TCM

TOM=0..0

00 9 I = l.NC TCM

DO 3 J = 1,NC

» - IC(I» TCM

N = ID(J) TCM

NUM = (VCI{"^)»»(l./3.)) * (VCI(N)**(l./3.)) TCM

59
NUM = SORTfNUMl TCM

OEN = <0.5)»( (VCI (Ml

*

<l./3. ) »* (VCI«N)»»f 1./3.)

n

MUM - NIJM / n FN TCM

NUM = NUH»»(3.)

AKTJ = (l.il) - NIIM TCM

TCIJ = (1.0 - AKIJl SOPTCTCTd) •TCT(J)»1.8»1.8)

THM-sTOM + THfH •TH<JJ*TrTJ

TCM

3q CONTINUE

CONTINUE

TCM

TCM

TCMP=TDM«-10.

TCT = 0 TPM

10 TPO=TOM+10.

TP = ?T*1.81/TCMP TCM

NUM = (2901.01) -( (5738.92)*TP» (< 2849.85) •TR'»T«?> TCM

NUM = NUM (TP - (1.0) ) IF f NUM. LT . t-1 80 . > ) 00 = 0 TCM

TPM

IF(NU».LT. (-180.) » GO TO 11

00 = FXP(NUM)

TCM

TPM

THE STATEMENT ABOVE MAY "ESULT IN AN UNOEPFLOW SENSE LIGHT

ON STM^ nPFPATTNG "^y^TFM^ WHFN T HF MtlMOlFP MUM i 1 aPr;F TCMTPM 1 vj n NEGATIVE NUMBER. THE LARGE NEGATIVE VALUE IS PROPER AND

-Tup rnPPFPT flw';wFo Fnp no 7Fsn.

TCM

TPM

11 TCMP = TOM »• ( (TMC-TOM) »00)

TFST = (l.n) - (TCMP/TPO) TPM

TEST = ABS(TEST)

TF ( TE*;T .LT . ( . nn at » I GO TO 1?

TCM

TCM

ICT = ICT 1 TCM

TPM

TOO = TCMP

GO TO 10

TCM

TCM

12 TMC = TGMP/(1.3)

RETURN

TCM

TCM

ENO TCM

SUBROUTINE SLOCK

TYPE PESL KIJ,flJI

OIMENSICN <IJ(6,5 > , A JI (6,6)

COMMON /PAP/ KIJ.AJI OATA

0 <TA KIJ/

•0 .0 0 0 00 0,. 293E-a7,.g88E-07, .58ifE-06, 0 . 001 00 0, 0. 0010 00, 1.0 38608,

OATA

OATA

*Q. 0 00 0 0 0, .0537605,. 7(*',E-06, .2?3£-03, .ISi^E-O 5,1. 08826«», 1.029639,

•O.0 0C30G, .'0 3E-07,.22t*F-C6,.251E-06, .9g066itO , 1 . 13956U , 1 . 3 10 1 92

,

OATA

OATA

'0.0 0000 3, .i»i.0E-O7,.'»95E-07, 0.995000, 1.337282, .9867502,. 9638072,

•G. 000 00 0, . 310F-05,0. 995 0 00,1.121902,1.016 260, . 9992935 ,. 9'* 35 2 20 , OATA

OATA

0. onoQoo/

OATA ajT/

OATA

OATA

»C. a 3 00 0 0, .I&IE-Oi*, .98aF-a6, .4'»3E-05 , 0 . 00100 0, 0. 0010 00, 1. 01'»967,

0. OQCOO 0, .000 2tf62,.336F-06,.g98E-06, . 00 00 297 , 1 . 00731'», 1.0 08772,

OATA

OATA

»0 . 0 000 0 3, .6Q3E-35 ,.0 0 00 226, .666 E-06 ,1.001711, 1.010 832, 1.0 01911,

0. 3 00 03 0, .622E-05,. 2 3 OE-G 5, 0,995 0 00, 1.02790 9, 1.00 3225,. 99872 13,

OATA

OATA

0. 30C00C, .317 £-05,0.9950 00,1. 0158 70, 1 .005915, 1. 00 l!»21,.996897£f,

•0 .30000 0/

OATA

OATA

RETURN

ENO OATA

60
NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR 77-867

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

A COMPARISON OF MATHEI-IATICAL MODELS FOR THE PREDICTION

OF LNG DENSITIES

5. Publication Date October 1977

6. Performing Organization Code

2 75.02

7. AUTHOR! S) Robert D. McCarty

8, Performing Organ. Report No.

9. PERFOR.MING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/ Task/Work Unit No. 2751574

11. Contracty Grant No. BR-50-11

12. Sponsoring Organization Name and Complete Address (Street, City, State, Z.IP) American Gas Association

1515 Wilson Boulevard

Arlington, VA 22209

13. Type of Report & Period

Covered

14. Sponsoring .\gency Code

15. SUPPLE.MENTARV NOTES

16. ABSTRACT (A 200-word or less factual summary of most si^ificant 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 compared. i Each model has been optimized to the same experimental data set. The experimental data

j consist of over 175 new PVTx data points taken in this laboratory. The objective of the;

study was to obtain a mathematical model which would predict LNG densities to within j 0.1% of the true value. The extent to which the objective has been achieved is not ' clear at this time. Additional experimental data are needed to resolve some j discrepancies between the present data and all models investigated to date. Computer [ program listings for all four models are presented.

'17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Computer program; density; equation of state; LNG; mixtures; PVTx.

18. AVAILABILITY : X Unlimited 19. SECURITY CLASS

(THIS REPORT)

21. NO. OF P.AGES

' For Official Distribution. Do Not Release to NTIS

UNCLASSIFIED

66

[ Order From

Washington

Sup. of Doc, U.S. Government

D.C. 20402. SD Cat. No. CL^

Printing Office 20. SECURITY CLASS

(THIS PAGE)

22. Pric

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National Technical Information

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UNCLASSIFIED $5 . 25

USCDMM.OC 29342-P74