REAL-GAS E

by Robert C. Johnson Lewis Research Center

TEC P-INICAL Symposium on Flow - Its Measurement and Control in Science and

ER proposed for presentation at

sburgh, Pennsylvania, May

https://ntrs.nasa.gov/search.jsp?R=19710009158 2018-05-21T17:48:10+00:00Z

r- W r i W

I w

Real-Gas Effects i n Flow Metering

Robert C. Johnson

National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio 44135

Methods of computing the mass-flow r a t e of nonperfect gases

a r e discussed.

sonic-flow nozzle a r e given f o r a i r , nitrogen, oxygen, normal

and para-hydrogen, argon, helium, steam, methane, and n a t u r a l

gas . The pressure ranges t o 100x10 N/m (- 100 atm) . For

steam, the temperature range i s from 550 t o 800 K. For t h e

o ther gases, t h e temperature range i s from 250 t o 400 K O

Data f o r computing mass-flow r a t e through a

5 2

INTRODUCTION

When flow meters a r e used f o r measuring t h e mass-flow r a t e of gases,

e r r o r s may a r i s e i f t h e flow r e l a t i o n s t h a t a r e used i n data reduction

involve t h e assumption t h a t t h e gas i s per fec t . For t h i s report , a

p e r f e c t gas i s defined as one having an invar ian t s p e c i f i c hea t and a

compressibil i ty f a c t o r of uni ty . A p e r f e c t gas i s t o be dis t inguished

from an i d e a l gas, which has a temperature-dependent s p e c i f i c heat and

uni ty compressibil i ty f a c t o r . A nonperfect gas i s a r e a l gas. The

assumption t h a t the gas i s p e r f e c t i s s u f f i c i e n t l y accurate f o r computing

2

t h e flow of such gases as a i r and nitrogen a t atmospheric pressure and room

temperature. However, for gases a t high pressure or low temperatures,

s i g n i f i c a n t e r r o r s w i l l r e s u l t i f t h e perfect-gas flow r e l a t i o n s a r e used.

There a r e a number of cases where the real-gas correct ions a r e simple

t o apply. For thesevcases , the changes i n pressure and temperature of t h e

gas as it flows through the meter a r e much smaller than the respect ive

absolute l e v e l s of pressure and temperature; the flow can then be considered

incompressible. It i s then only necessary t o know the gas density,which can

be determined from t h e pressure and temperature. I n references [l, 2, and 31

t h e d e n s i t i e s or compressibil i ty f a c t o r s of some common gases a r e tabulated

as functions of pressure and temperature. For these cases, t h e real-gas

correct ion cons is t s of using an accurate value of densi ty r a t h e r than a

value t h a t would r e s u l t from assuming t h e gas t o be p e r f e c t .

density can be calculated from an equation o f s t a t e , or e l s e obtained from

a tabula t ion , such as references [l, 2, or 31, of densi ty or compressibil i ty

fac tor a s a function of pressure and temperature. Two examples where

incompressible flow may be assumed are :

The cor rec t

1. A volumetric flowmeter such as a turbine-type meter where t h e

pressure drop across the meter i s much smaller than t h e absolute

l e v e l of pressure.

A head-type meter such as a nozzle or o r i f i c e operating a t a high

pressure l e v e l where the pressure drop across t h e meter i s much

smaller than t h e absolute l e v e l of pressure.

2.

The mater ia l presented i n t h i s repor t appl ies t o head-type flowmeters

through which t h e flow can be considered one-dimensional and i sen t ropic .

3

Two such flowmeters a r e the nozzle and t h e ventur i . I n both of these meters,

the flow from t h e upstream plenum t o the flowmeter t h r o a t can be considered

one-dimensional and i sen t ropic t o a good approximation. Actual deviations

from these conditions can be 'handled by applying a multiplying f a c t o r ( t h e

discharge c o e f f i c i e n t ) tha t i s almost unity, and i s a function of Reynolds

number.

t o a s u f f i c i e n t degree t o permit r igorous appl ica t ion of the data developed

here.

?"ne flow through an o r i f i c e i s ne i ther one-dimensional nor i sen t ropic

While the conventional i sen t ropic flow equations apply t o a per fec t gas,

a number of inves t iga tors have considered t h e i sen t ropic flow of nonperfect

gases. References [4 and 51 develop equations f o r calculat ing t h e i sen t ropic

flow of gases described by t h e Van der Waalsequation of s t a t e . A method of

ca lcu la t ing the flow of nonperfect diatomic gases using Berthelot ' s s t a t e

equation i s described i n reference [ 6 ] . I n references [7, 8, and 91, t h e

authors consider t h e flow of gases described by the Beattie-Bridgeman

equation of s t a t e . I n addition, reference [9] presents t a b l e s of functions

t h a t a i d i n the one-dimensional flow calculat ions of r e a l a i r . References

[lo and 111 present methods of estimating i sen t ropic exponents t o be used

f o r ca lcu la t ing t h e flow of imperfect gases through sonic-flow nozzles.

( A sonic-flow nozzle i s one i n which the t h r o a t ve loc i ty equals the l o c a l

speed of sound. A sonic-flow nozzle has a l s o been ca l led a choked nozzle

or a cr i t ica l - f low nozzle . ) Reference [12], using the tabulated data of

reference [l], presents a graphical method f o r computing the i sen t ropic

mass flow r a t e of imperfect gases. I n reference [l3], t h e author reviews

t h e sonic-flow meter and suggests methods f o r correct ing f o r gaseous

4

imperfections.

one-dimensional flow of imperfect gases i s given. The program involves the

in t e rpo la t ion of s e t s of thermodynamic-property data t h a t a r e s tored i n t h e

computer. These same authors have published a s e t of t a b l e s ( r e f . [l?]), for

ca lcu la t ing t h e one-8imensional flow proper t ies of r e a l a i r .

dynamic da ta f o r a i r t h a t a r e involved i n reference [15] a r e t h e da ta

tabulated i n reference [ l ] .

reference [16].

mass-flow r a t e of a i r , N

t o be ca lcu la ted .

r a t e ca lcu la t ion when t h e nozzle i s operated subsonically.

t h e a i r , N2, 02, n-H2, and H20 data of reference [ l 7 ] a r e presented i n

tabular form; p-H2 da ta a r e a l s o presented.

t h a t permit ca lcu la t ing the mass-flow r a t e of N

nozzles. Reference [3] d i f f e r s from references [ 2 and IT] i n t h a t t h e

pressure and temperature ranges i n reference [3] a r e g rea t e r than the ranges

i n references [ 2 and 171. References [ 2 and 31 a l s o contain t a b l e s of such

thermodynamic p rope r t i e s a s compressibi l i ty f ac to r , spec i f i c hea t , and

speed of sound. I n addi t ion, reference [3] contains t h e computer programs

used i n making t h e ca lcu la t ions . I n reference [18], da ta for ca lcu la t ing

the flow o f na tu ra l gas through sonic-flow nozzles a r e presented; t h e

computer program for ca lcu la t ing these data i s given i n reference [lg].

I n reference [14], a computer program f o r ca lcu la t ing the

The thermo-

Sonic-flow functions f o r steam a r e given i n

Reference [l7] presents a set of graphs t h a t permit the

0 2 , n-H2, A, He, and H 0 through sonic-flow nozzles 2' 2

Information i s also given on how t o make t h e mass-flow

I n reference [ 2 ] ,

Reference [3] has tabulated data

and He through sonic-flow 2

I n t h i s repor t , t h e sonic flow data f o r various gases, a s presented

i n references [2, 3, 1.7, and 181, a r e summarized. Since these references

were published, more exact ca lcu la t ions for argon and methane have been made.

5

The more exact argon data replaces t h a t i n reference [l7], and t h e more

exact methane data replaces t h a t i n reference [18]. These data a r e presented

i n terms o f a sonic-flow f a c t o r . The use of t h i s f a c t o r permits t h e mass

flow rate of these gases through sonic-flow nozzles to be calculated. I n

addition, the empirzcal method, given i n reference [l7], of ca lcu la t ing the

mass-flow r a t e of these gases through subsonic nozzles, i s presented.

a l l gases except steam, t h e calculat ions a r e f o r temperatures from 250 to

400 K, and pressures to 100x10

500 to 800 K, and t h e pressures to 100x10

throughout t h i s repor t .

For

5 2 N/m . For steam, the temperatures a r e from

5 2 N/m , S.I. 1960 u n i t s a r e used

A

a

C P

C V

G

H

m

P

R

S

T

SYMBOLS

2 area, m

speed of sound, m/sec

s p e c i f i c heat a t constant pressure, m / (see

s p e c i f i c heat a t constant volume, m / (see

mass flow r a t e per unit area, kg/(m2 see)

enthalpy, m /see

i n t e g r a t i o n constants f o r enthalpy, K

in tegra t ion constants f o r entropy

mass flow r a t e , kg/sec

pressure, N/m

gas constant, m2/(sec K)

entropy, m / (see2 K)

temperature, K

2 2 K) 2 2 K)

2 2

2

2

2

6

V

Z

Y

Subs crip t s

0

i

P

velocity, m/sec

compressibility factor

specific-heat ratio

sonic-flow factor defined implicitly by equation 12, (see K2)/m 1

.o

refers to plenum station

refers to nozzle throat station

refers to ideal-gas condition

refers to perfect-gas condition

ANALYSIS

The conditions assumed in this analysis are as follows: The gas

is at rest in a plenum and accelerates one-dimensionally and isentropically

to the throat of a nozzle where its speed is sonic. The measured quantities

are the plenum pressure and temperature. The gas is not assumed to be

perfect, and its state equation is given by

p = ZpRT (1)

where Z is the compressibility factor and may be expressed as a function

of pressure and temperature or of density and temperature. The assumption

that the flow is one-dimensional and starts from rest is represented by

The assumption that the flow is isentropic is represented by

s = s 0 1

and the fact that the flow is sonic is represented by

v1 = al

7 I n order t o solve equations (1) through (4), it i s necessary t o express

enthalpy, entropy, and the speed of sound i n terms of e i t h e r pressure and

t e a p e r a t w e , or densi ty and temperature, depending on t h e form of t h e

s t a t e equation.

Case I. Z = Z(p,T)

The expressions f o r enthalpy and entropy a r e integrated forms of Eqs.

( 4 ) and ( 5 ) i n reference [l?].

P - - H R - k, R dT - T I [I.(%)]&+% P

P 0

( 5 )

The te rqera ture i n t e g r a l s i n Eqs. (5 ) and (6) a r e i n d e f i n i t e i n t e g r a l s whose

constants of in tegra t ion a r e included i n % and KS. The values o f % and KS

and (6) a l s o involve t h e ideal-gas s p e c i f i c hea t . The term ideal-gas r e f e r s

t o a gas whose compressibil i ty f a c t o r i s invar ian t , with a value of unity;

however, unlike a p e r f e c t gas, the s p e c i f i c hea t i s a funct ion of temperature.

This condition i s approached as t h e pressure of t h e gas approaches zero,

providing d issoc ia t ion does not occur.

i s found i n reference [l7]. The value of a i s obtained from

depepd on the choice of the gas reference s t a t e . Equations ( 5 )

The expression f o r t h e speed of sound

ZzRT/az = Z - ( $9T - (7)

where

8

If these expressions for enthalpy, entropy, and speed of sound a r e subs t i tu ted

i n Eqs. ( Z ) , (3) , an; (4), and t h e i t e r a t i o n procedures given i n reference

[l7] a r e then applied, solut ions can be obtained for the veloci ty , pressure,

and temperature a t t h e nozzle t h r o a t .

a t t h e nozzle throa t , t h e corresponding densi ty i s determined through Eq. (1).

The mass flow r a t e per un i t area through t h e sonic-flow nozzle then becomes

Knowing the pressure and temperature

Case 11. Z = Z(p,T)

The expressions for enthalpy and entropy a r e given i n reference [3] and

are :

The expression for t h e speed o f sound i s found i n reference [l7].

value of a i s obtainable from

The

where

9

These expressions f o r enthalpy, entropy, and speed of sound a r e subs t i tu ted

i n Eqs. ( 2 ) , ( 3 ) , and (4).

plenum density, and f o r density, temperature, and veloci ty a t t h e nozzle

Equations (1) through ( 4 ) a r e then solved f o r .?

th roa t . The i t e r a t i o n procedures involved i n t h i s solut ion a r e found i n

reference [ 3 ] . The expression f o r t h e mass-flow r a t e per u n i t area through

t h e sonic-flow nozzle i s again given by equation (9) .

RESULTS AND DISCUSSION

The Sonic-Flow Factor

The mass flow r a t e of gases through sonic flow nozzles can be expressed

i n terms of a sonic-flow fac tor , 0, as follows:

For a per fec t gas, the value

of pressure and temperature and i s given by

QP o f t h i s sonic-flow f a c t o r i s independent

where Tp

and para-hydrogen; 5/3 f o r argon and helium; and 4/3 f o r steam, methane,

i s chosen t o be 7/5 f o r a i r , nitrogen, oxygen, normal hydrogen,

and n a t u r a l gas.

For an i d e a l gas, the sonic-flow f a c t o r has a value Qi that i s

a funct ion of temperature and is given by

@. = l i m @ 1

10

(16)

The r e s u l t s of t h e real-gas calculat ions a r e presented graphical ly i n

Instead of p l o t t i n g t h e sonic-flow f a c t o r as a function Figs. (I) t o (3 ) .

of pressure and temgerature t h e r a t i o of t h e real-gas sonic-flow f a c t o r t o

t h e ideal-gas sonic-flow fac tor i s p l o t t e d . The reason f o r t h i s i s t h a t ,

i f the sonic-flow f a c t o r i t s e l f were p lo t ted , t h e famil ies of curves would

cross each o ther f o r some of t h e gases, making t h e graphs d i f f i c u l t t o

read.

t h e sonic mass-flow r a t e i s

I n terms of the ordinates i n Figs. (1) t o (3) , t h e expression f o r

where t h e values of Qi a r e given on the f igures t o which they apply.

I n t h e event t h a t it i s desired t o use nozzles or ventur ies subsonically,

but t h e v e l o c i t i e s are such t h a t t h e flow has t o be considered compressible,

t h e following equation, derived from Eq. (27) i n reference [l’j’], appl ies

Equation (18) i s not based on theory, but i s an approximation t o a c t u a l

subsonic calculat ions. For t h e pressure and temperature ranges involved,

Eq. (18) reproduces t h e subsonic ca lcu la t ions t o within $ percent f o r the

gases considered i n t h i s r e p o r t .

f igures t o which they apply. The values o f t h e compressibil i ty f a c t o r

The values ( Oi/QP) are given on t h e

a r e given graphical ly i n Figs. ( 4 ) t o (6) f o r t h e gases considered i n

11

t h i s r epor t . The perfect-gas mass-flow r a t e 5 i s given by

I n Figs . (1) ta, (3) , ( @/Qi) i s p lo t t ed as a funct ion of P and T

2, 02, n-H2, p-H2, A, He, H 0, CH4, and na tu ra l gas. f o r a i r , N

i n t e r e s t i n g r e s u l t s i n Fig. (2a ) i s t h a t even though the sonic-flow fac to r s

f o r n-H

over t h e range of pressures and temperatures considered, t h i s r a t i o i s

independent of temperature.

One of t he 2

and p-H 2 2 a r e d i f f e r e n t , t he r a t i o (@/Qi) i s t h e same; fu r the r ,

The na tura l gas da ta i n Fig, (3b) a r e f o r a p a r t i c u l a r composition.

Therefore, t h i s data would not apply s t r i c t l y to a na tu ra l gas of a d i f f e r e n t

composition. However, s ince methane i s usual ly the p r inc ipa l component of

na tu ra l gas, t h e sonic-flow fac to r s o f na tu ra l gases approximate those of

methane.

Table I l i s t s the sources o f the data presented i n Figs. (1) t o (3) ,

a s wel l a s t h e references f o r the compressibi l i ty-factor and ideal-gas

spec i f ic -hea t data t h a t were used i n the ca lcu la t ions .

The pressure and temperature rariges covered by some of t he references

exceed t h e ranges covered i n t h i s r epor t . Table I1 l i s t s the a c t u a l ranges

covered i n references [2, 3, 17, and 181.

Compressibility-Factor Data

I n order t o use Eq. (18), it i s necessary to have compressibi l i ty-factor

da ta . To t h i s end, Figs. (4) to (6) a r e presented. Pressure and temperature

ranges a r e t h e same a s i n the sonic-flow r a t i o f igu res (F igs . (1) to ( 3 ) ) .

REFmENCES 1 2

'5. Hilsenrath, e t al., Tables of Thermodynamics and Transport Propert ies

of A i r , Argon, Carbon Dioxide, Carbon Monoxide, Hydrogen, Nitrogen,

Oxygen, and Steam (Pergamon Press, New York, 1960).

2R. C. Johnson, R e a l - G a s Ef fec ts i n C r i t i c a l Flow Through Nozzles and

Tabulated Ther?nodynamic Properties, NASA TN D-2565 (1965).

3R. C. Johnson, Real-Gas Effec ts i n C r i t i c a l Flow Through Nozzles and Thermo-

dynamic Propert ies of Nitrogen and Helium a t Pressures t o 3O0X1O5 Newtons

per Square Meters (Approx 300 atm), NASA SP-3046 (1968).

4H.-S. Tsien, One Dimensional Flows of a Gas Characterized by Van de r

Waal's Equation of S ta te , J. Math phys. 25, 301 (1947).

5C. duP. Donalson, Note on the Importance of Imperfect-Gas Effec ts

Variation of Heat Capacities on the Isentropic Flow of Gases.

RM L8J14 (1948)

6A. J. Eggers, Jr., One-Dimensional Flows of an Imperfect Diatomic

TN 1861 (1949) (.

7J. C. Crown, Flow of a Gas Characterized by t h e Beattie-Bridgeman

and

NACA

Cas, NACA

Equation

of S t a t e and Variable Spec i f ic Heats; P a r t I - Isentropic Relations,

Naval Ordnance Laboratory Memo 9619 (Apr. 22, 1949).

'R. E. Randall, Thermodynamics Propert ies of Gases: Equations Derived from

t h e Beattie-Bridgeman Equation of S t a t e Assuming Variable Spec i f ic

Heats, Arnold Engineering Development Center 733-57-10, 0-135332

(Aug. 1957)-

'R. E. Randall, Thermodynamics Propert ies of A i r : Tables and Graphs D e -

r ived from the Beattie-Bridgeman Equation of S t a t e Assumzng Variable

Spec i f ic Heats, Arnold Engineering Development Center 733-57-8, AD-135331,

(Aug5 1957).

13

''Ao S. Ibe ra l l , The Effec t ive 'Gamma' f o r Isentropic Expansion of R e a l

Gases, J. Appl. Phys. l.9, 997 (19481,

"W- C. Edminster, Applied Hydrocarbon Thermodynamics, Par t 30 - Isen-

t r o p i c Exponents and Critical-Flow Metering, Hydrocarbon Processing

2 46 139 (19673.

"R. M. R e i m e r , Computation of the Critical-Flow Function Pressure Ratio,

and Temperature R a t i o s f o r Real A i r , J. Basic Eng. 86, 169 (1964).

'%. T. Arnberg, Review of the Critical-Flow Meter f o r Gas Flow Measpements,

J. Basic Eng. 84, 447 (1962).

'%I. D. Mintz and D. P. Jordan, Procedure for Dig i t a l Computer Analysis of One

Dimensional Fluid-Flow Processes Involving Real Gases, Lawrence

Radiation Laboratory Report UCRL-7530 (Jan. 19641

'%. P, Jordan and M. D. Mintz, A i r Tables (McGraw-Hill Book Co., Inc.,

New York, 1965).

16J. W. Murdock and J. M. Bauiran, The C r i t i c a l Flow Function f o r Superheated

Steam, 5. Basic Eng., 3 507 [1964),

17R, C. Johnson, Calculations of Real-Gas Effec ts i n Flow Through Cr i t i ca l -

Flow Nozzles, J. Basic Eng., €%, 519 (1964).

18R. C. Johnson, Calculations of the Flow of Natural Gas Through C r i t i c a l

Flow Nozzles, J. Basic Eng. 92, 580 (1970).

19R. C . Johnson, A S e t of FORTRAN IV Routines used t o Calculate the Mass Flow

Rate of Natural Gas Through Nozzles, NASA TM X-2240 (1971).

2oH. W, Woolley, R. B. Scot t and F. G. Brickwedde, Computation of Thermal

Propert ies of Hydrogen i n I ts Various Isotopic and Ortho-Para

Modifications, J.. R e s . N a t . Bur. Std.. ( U . S . ) 41, 379 (1948).

14 21A. L. Gosman, R. D. McCarty and J. G. Hust, Thermodynamic Propert ies of

Argon From t h e Tr ip le Point t o 300 K a t Pressures t o 1000 Atmospheres,

National Bureau of Standards NSRDS-NBS-27 (1969).

“D. B. Mann, The Thermodynamic Properties of Helium from 3 t o 300 K Between

0.5 and 100 Atmospheres, National Bureau of Standards Tech. Note 154

(1962) e

23F. G. Keyes, The Consistency of the Thermodynamic Data for Water Substance

Vapor Phase t o 550° C, p a r t V I I , J. Chem. Phys. -9 1 7 923 (1949).

24A. J. Vennix and R. Kobayashi, An Equation of S t a t e for Methane i n t h e Gas

and Liquid Phases, AIChE J. -, 15 926 (1969).

2%. S. McDowell and F. H. Kruse, Thermodynamic Functions of Methane, J. Chem.

Eng. D a t a E, 547 (1963).

26M. Benedict, G. B. Webb and L. C. Rubin, An Empirical Equation f o r Thermo-

dynamic Propert ies of Light Hydrocarbons and Their Mixtures - Constants

for Twelve Hydrocarbons, Chem. Eng. Progr. 47, 419 (1951).

27C. T. Sciance, C, P. Colver and C. M. Sliepcevich, Bring Your C1-C4 D a t a

up t o Date, Hydrocarbon Processing 46, 173 (19671.

28Anon., Technical Data Book - Petroleum Refining (American Petroleum

I n s t i t u t e , New York, 1966) e

Gas

A i r

*2

O2

2 n-H

P-H2

A

He

H2°

CH4 Nat. Gas

15 Table I. Data References

Sonic-Flow Factor

3

Compressibility Factor

1

1

1

20

20

2 1

22

23

24

18,19,26

Ideal-Gas Spec i f ic Heat

1

1

( a ) These data a r e presented i n t h i s repor t f o r t he f i rs t time.

1 6

Gas

A i r

N2

O2

n-HZ

P-H2

A

He

H2°

CH4

Nat. gas

Table 11. Pressure and Tern e r a t u r e Ranges Covered i n References. Pressures i n 105 N/m’ (- a t m ) ; Temperatures i n K.

Ref. 2 Ref. 3 Ref. 17 R e f . 18 ( Tables ) (Tables ) (Graphs ) ( Tables )

FIGURE LEGENDS

(a) Air.

(b) Nitrogen.

(c) Oxygen.

Figure 1. - Ratio of the real-gas sonic-flow factor to the ideal-gas sonic- flow factor for various gases.

(a) Hydrogen.

(b) Argon.

(c) Helium.

Figure 2. - Ratio of the real-gas sonic-flow factor to the ideal-gas sonic-flow factor for various gases.

(a) Methane.

(b) Natural gas (fractional composition by volume, CH4-0.9272, C2Hb-O. 0361, C3H8-0. 0055, iC4H10-0. 0007, nC4H10-Q OOlQ, N2-0. @18, C02-0. 0077).

Figure 3. - Ratio of the real-gas sonic-flow factor to the ideal-gas sonic - flow factor for various gases.

(a) Air.

(b) Nitrogen.

(c) Oxygen.

Figure 4. - Compressibility factor for various gases.

(a) Normal and para hydrogen.

(b) Argon.

(c) Helium.

(d) Steam.

Figure 5. - Compressibility factor for various gases,

(a) Methane,

(b) Natural gas- (composition i s the same as in fig. 3(b)),

Figure 6. - Compressibility factor for various gases.

- 250 400

I

4 Y

1.00 (A) AIR.

.03974 1.000

300 .03974 LOO0 1.06 350 .03974 1.000- 250

1.04

1.02

1.00 (B) NITROGEN.

.04246 1.000

.04245 .999

.04240 .998

PLENUM PRESSURE, N/m2

(C) OXYGEN.

Figure 1

0- - I-

d

(C) HELIUM.

PLENUM Pi P i l s P p

ATURE, -TEMPER- SEC ~ 1 / 2 / ~

- 600 1 . 1 0 ~ K 550 0.03113 0.9 MN] .03108 .9 650 .03103 .9

7% .03094 .9

PLENUM PRESSURE, N/m2

(D) STEAM.

Figure 2

K

250 0.02951 0.998 275 .OB46 .996 PLENUM 300 .OB40 .994 TEMPER - 350 .OB25 .989 ATURE, 400 .OB07 .983 K

- z (A) METHANE. ar 250 .03054 .996

275 .03049 .994 3 300 .03042 .992 3 350 .03025 .986 2 400 .03006 .980

rx

e 0

PLENUM PRESSURE, N/mZ

( B ) NATURAL GAS (FRACTIONAL COMPOSITION BY VOLUME, CH4-0. 9272, C2H6-0. 0361, C3H8-O. 0055, iC4HI0-0. W07,

Figure 3

nC4H10-0. 0010, N2-0.0218, CO2-0.0077).

(6) NITROGEN.

PRESSURE, N/m2

(C) OXYGEN.

Figure 4

TEMPER- 1.08

1.04

1.00 (A) NORMAL AN 6 PARA HYDROGEN.

TEMPER- ATURE,

(B) ARGON. z

PRESSURE, N/mL

(D) STEAM.

Figure 5

N

(A) METHANE.

PRESSURE, N/mz

(B) NATURAL GAS- (COMPOSITION IS THE SAME A S IN FIG. 3(B)).

F igure 6