SECTION 23

Physical Properties

This section contains a number of charts, correlations, and

calculation procedures to be used for predicting physical prop-erties of hydrocarbons and components found with them.Fig. 23-1 shows the nomenclature used in this section.

Fig. 23-2 is a table containing frequently used physical prop-erties for a number of hydrocarbons and other selected com-

B = second virial coefficient for a gas mixture,[kPa (abs)]-1

B′ = mole fraction H2S in sour gas stream, Eq 23-6Bii = second virial coefficient for component iBij = second cross virial coefficient for components i

and jbi

1/2 = summation factor for component iCABP = cubic average boiling point, °C

d = density, g/ccG = relative density (gas density)Gi = relative density (gas gravity) of ideal gas, MW/MWa

Giid = molecular mass ratio of component i in mixture

Hv = gross heating value per unit volume of ideal gas,MJ/m3

Kw = Watson characterization factor, Fig. 23-12k = thermal conductivity, W/(m • °C)

ka = thermal conductivity at one atmosphere, W/(m • °C)M = mass fractionm = mass, kg

MW = molecular mass, g moleMABP = molal average boiling point, °C or K

MeABP = Mean average boiling point, °C or Kn = number of moles (mass/mole weight)P = pressure, kPa (abs)

Pc′ = pseudocritical pressure adjusted for acid gascomposition, kPa (abs)

Pvp = vapor pressure at a reduced temperature of 0.7Pw

o = vapor pressure of water, 7.3811 kPa (abs) at 40°CR = gas constant, 8.3145 [kPa (abs) • m3]/(K • kg mole)

for all gases (see Section 1 for R in other units)S = relative density at 15°/15°CT = absolute temperature, Kt = ASTM D-86 distillation temperature, °C or K,

Eq 23-11Tc′ = pseudocritical temperature adjusted for acid gas

composition, KV = volume, m3

VABP = volumetric average boiling point, °C

FIG

Nomen

2

ponents. Immediately following is a detailed list of referencesand footnoted explanation for the values in Fig. 23-2.

Physical properties for eighteen selected compounds can befound in GPA Standard 2145, "Table of Physical Constants ofParaffin Hydrocarbons and Other Components of NaturalGas."

W = mass, kgWABP = weight average boiling point, °C

yi = mole fraction of component i from analysis on drybasis, Eq 23-37

x = mole fraction in liquid phaseyi

w = mole fraction of component i adjusted for watercontent

y = mole fraction in gas phaseZ = compressibility factor

Greekε = pseudocritical temperature adjustment factor,

Eq 23-6θ = MeABP/Tpc

ρ = density, kg/m3

µ = viscosity at operating temperature and pressure,centipoise

µA = viscosity at 101.325 kPa (abs) (1 atm) and operatingtemperature, centipoise

ξ = factor defined by Eq 23-20σ = surface tension, dynes/cmω = acentric factorη = kinematic viscosity, centistokes

Subscriptsa = airb = boilingc = criticali = component i

L = liquidm = mixturepc = pseudocritical

r = reduced stateV = vaporv = volumew = water

Superscriptsid = ideal gasw = water

o = reference state

. 23-1

clature

3-1

s

See Note No.

Compound

MethaneEthanePropanelsobutanen-Butane

Isopentanen-PentaneNeopentane

n-Hexane2-Methylpentane3-MethylpentaneNeohexane2,3-Dimethylbutane

n-Heptane2-Methylhexane3-Methylhexane3-Ethylpentane2,2-Dimethylpentane2,4-Dimethylpentane3,3-DimethylpentaneTriptane

n-OctaneDiisobutylIsooctanen-Nonanen-DecaneCyclopentaneMethylcyclopentaneCyclohexaneMethylcyclohexane

Ethene(Ethylene)Propene(Propylene)1-Butene(Butylene)cis-2-Butenetrans-2-ButeneIsobutene1-Pentene1,2-Butadiene1,3-ButadieneIsoprene

Ethylbenzeneo-Xylenem-Xylenep-Xlyene

Isopropylbenzene

Methyl alcoholEthyl alcoholCarbon monoxideCarbon dioxideHydrogen sulfideSulfur dioxide

AmmoniaAirHydrogenOxygenNitrogenChlorineWaterHeliumHydrogen chloride

16.043 -161.5130.070 -88.5944.097 -42.0758.123 -11.7958.123 -0.51

(35000)*

1369.8530.89379.61

-182.45* 4599.-182.79* 4880.-187.62" 4240.-159.59 3640.-138.35 3784.

72.150 27.83 151.31114.70

-159.89 3381.72.150 36.05 -129.71

270.03365.

72.150 9.50 -16.58 3199.

86.177 68.7286.177 60.2486.177 63.2686.177 49.7286.177 57.96

37.297 -95.3150.6845.73

-153.67-162.89

73.4155.34

-99.825-128.53

3030.3010.3120.3080.3130.

100.204 98.37 12.342100.204 90.03 17.226100.204 91.85 16.155100.204 93.47 15.265100.204 79.17 26.32100.204 80.47 24.85100.204 86.04 20.94100.204 80.86 25.41

-90.55-118.26

-118.58-123.78-119.21-134.44

-24.56

2740.2730.2810.2890.2770.2740.2950.2950.

114.231 125.65114.231 109.08114.231 99.21128.258 150.78142.285 174.1170.134 49.2284.161 71.8384.161 80.7898.188 100.94

4.146 -56.768.417

12.966-91.160

-107.351.358 -53.480.4814 -29.63

73.99 -93.82733.75 -142.4324.64 6.55012.211 -126.59

2490.2490.2570.2280.2100.

425.

4508.3784.4073.3471.

28.054 -103.7342.081 -47.6856.108 -6.2356.108 3.7256.108 0.8856.108 -6.9170.134 29.9554.092 10.8454.092 -4.4168.119 34.05

(9700)

459.0338.3366.5477.4141.65269.436.1123.8

-169.15*-185.25*-185.35*-138.90-105.54-140.34-165.21-136.19-108.89-145.95

5040.4665.4043.4243.3964.4000.3513.

(4502)

(3856)

26.038 -84.01*78.114 80.0792.141 110.60

106.167 136.17106.167 144.39106.167 139.09106.167 138.32104.152 145.23120.194 152.38

24.387.8952.8732.0512.5282.6482.001.47

-80.8"5.532

-94.98-94.963-25.18-47.8613.2630.63

-96.021

6139. 308.31 0.004324898. 562.12 0.003324106. 591.76 0.003433606. 617.16 0.003523734. 630.29 0.003483536. 617.01 0.003543511. 616.19 0.003574050.3209.

(646)* 0.003330.00355

32.042 64.6746.069 78.2628.010 -191.4544.010 -78.464*34.082 -60.26664.065 -9.94

35.4417.903

—

2859.7630.2

-97.65 8097.-114.1 6148.-204.99* 3494.

-56.56* 7374.-85.48* 8963.-75.47* 7884.

17.0305 -33.3228.9625 -194.34

2.0159 -252.850*31.9986 -182.954*28.0134 -195.79870.9054 -33.9518.0153 99.974*

4.0026 -268.9536.461 -85.14

1555.———

1146.7.3849

6547.

-77.69*

-259.347*-218.792*-209.997*-100.95

0.000

-114.17*

11350.3771.1293.5043.3398.7977.

22064.227.5

8310.

PHYSICAL CONSTANTS *See the Table of Notes and Reference

Critical constants

190.56 0.00617305.41 0.00489369.77 0.00454407.82 0.00446425.10 0.00439

460.35 0.00427469.65 0.00434433.71 0.00420

506.4 0.00429497.46 0.00426504.4 0.00426488.66 0.00417499.86 0.00415

539.2 0.00426530.06 0.00420535.16 0.00403540.46 0.00415520.36 0.00415519.66 0.00417536.26 0.00413531.06 0.00397

568.4 0.00420549.96 0.00422543.86 0.00410594.7 0.00433617.7 0.00439511.6 0.00371532.75 0.00379553.5 0.00366572.15 0.00375

282.34 0.00466365.55 0.00448419.92 0.00426435.54 0.00417428.59 0.00424417.86 0.00425464.74 0.00421

(444)* (0.0043)*

(484)0.00407

(0.0041)*

512.60 0.00368513.88 0.00362132.86 0.00329304.11 0.00214373.37 0.00288430.8 0.00190

405.5 0.00425132.43 0.0032333.0 0.03185*

154.59 0.00229126.21 0.00318416.86 0.00175647.10 0.003102

5.20 0.01436324.68 0.00222

12345

678

910111213

1415161718192021

222324252627282930

31323334353637383940

414243444546474849

505152535455

565758596061626364

12345

678

910111213

1415161718192021

222324252627282930

31323334353637383940

414243444546474849

505152535455

565758596061626364

(6000)*

—

4277.

AcetyleneBenzeneToluene

1691.

—

Styrene

—

—

— —

—

631.1

1.00040*1.21403*1.29558*1.3251*1.33631*

1.356581.360241.345*

1.377461.374171.379181.371571.37759

1.390171.387431.391191.395941.384751.384081.393421.39196

1.399811.394881.393921.407731.414111.409271.412401.428921.42566

(1.241)*1.313*1.351*1.368*1.359*1.358*1.3746

——

1.4253

—1.50431.499601.498561.507951.499801.498391.54961.49400

1.330281.363451.00036*1.00049*1.00061*1.00062*

1.00036*1.00028*1.00013*1.00027*1.00028*1.3878*1.333471.00003*1.00042

For

mul

a

Num

ber

Mol

ar m

ass

(Mol

ecul

ar w

eigh

t)

Boi

ling

Poi

nt, å

C10

1.32

50 k

Pa(

abs)

Vap

or p

ress

ure,

kPa(

abs)

, 40˚

C

NOTE: Numbers in this table do not have accuracies greater than 1 part in 1000; in some cases extra digits have been added to calculated values to achieve internal consistency or to permit recalculation of experimental values.

A. B. C. D.

Fre

ezin

g po

int,˚

C10

1.32

50 k

Pa(

abs)

Ref

ract

ive

inde

x,

n D 1

5˚C

Pre

ssur

e,kP

a(ab

s)

Tem

pera

ture

, K

Volu

me,

m3 /

kg

C H4 10

C H3 8

C H4 10

C H2 6

C H4

C H5 12C H5 12C H5 12

C H5 10

C H6 14C H6 14C H6 14C H6 14

C H6 12

C H7 16C H7 16C H7 16C H7 16C H7 16C H7 16C H7 16C H7 16

C H8 18C H8 18C H8 18C H9 20

C H7 14

C H2 4C H3 6C H4 8C H4 8C H4 8C H4 8C H5 10C H4 6C H4 6C H5 8

C H2 2C H6 6C H7 8C H8 10

8 10

8 10

8 10

C HC HC HC H8 8C H9 12

C H6 14

C H6 12

10 22C H

CH O4

2 6C H OCOCO2

HCl

H S2SO2

He

Cl2H O2

O2

H 2

N2

N2 O2+NH3

5/99

Num

ber

FIG. 23-2

Physical Constants

Revised (5-99)23-2

FIG. 23-2 (Cont’d)

Physical Constants

23-3

FIG. 23-2 (Cont’d)

Physical Constants

23-4

FIG. 23-2 (Cont’d)

Notes and References for the Table of Physical Constants

23-5

FIG. 23-2 (Cont’d)

Notes and References for the Table of Physical Constants

23-6

FIG. 23-2 (Cont’d)

Notes and References for the Table of Physical Constants

23-7

a. Values in parentheses are estimated values.b. The temperature is above the critical point.c. At saturation pressure (triple point).d. Sublimation point.e. The + sign and number following specify the number of cm3 of

TEL added per gallon to achieve the ASTM octane number of100, which corresponds to that of Isooctane (2,2,4-Trimethylpentane).

f. These compounds form a glass.g. Average value from octane numbers of more than one sample. h. Saturation pressure and 15°C. i. Index of refraction of the gas. j. Densities of the liquid at the normal boiling point. k. Heat of sublimation. m. Equation 2 of the reference was refitted to give:

a = 0.7872957; b = 0.1294083; c = 0.03439519. n. Normal hydrogen (25% para, 75% ortho).

p. An extrapolated value.

q. Gas at 15°C and the liquid at the normal boiling point.

r. Fixed points on the 1968 International Practical TemperatureScale (IPTS-68).

s. Fixed points on the 1990 International Temperature Scale(ITS-90).

t. Densities at the normal boiling point are: Ethane, 554.0 [29];Propane, 581.0 [28]; Propene, 609.1 [5]; Hydrogen Chloride,1192 [43]; Hydrogen Sulfide, 949.0 [25]; Ammonia, 681.6 [43];Sulfur Dioxide, 1462 [43].

u. Technically, water has a heating value in two cases: net((2.466 MJ/kg) when water is liquid in the reactants, and gross(+1.879 MJ/m3) when water is gas in the reactants. The valueis the ideal heat of vaporization (enthalpy of the ideal gas lessthe enthalpy of the saturated liquid at the vapor pressure).This is a matter of definition; water does not burn.

v. Extreme values of those reported by reference 19.

A. Molar mass (molecular mass) is based upon the followingatomic weights: C = 12.011; H = 1.00794; O = 15.9994; N =14.0067; S = 32.066; Cl = 35.4527. The values were roundedoff after calculating the molar mass using all significant figuresin the atomic weights.

B. Boiling point: the temperature at equilibrium between the liq-uid and vapor phases at 101.3250 kPa.

C. Freezing point: the temperature at equilibrium between the crys-talline phase and the air saturated liquid at 101.3250 kPa.

D. The refractive index reported refers to the liquid or gas and ismeasured for light of wavelength corresponding to the sodiumD-line (589.26 nm).

E. The relative density: ρ(liquid, 15°C)/ρ(water, 15°C). The den-sity of water at 15°C is 999.10 kg/m3.

F. The temperature coefficient of density is related to the expan-sion coefficient by: (∂ρ/∂T)P/ρ = –(∂ρV/∂T)P/V, in units of 1/T.

G. Pitzer acentric factor: ω = –log10(P/Pc) –1, P at T = 0.7 Tc H. Compressibility factor of the real gas, Z = PV/RT, is calculated

using the second virial coefficient.I. The density of an ideal gas relative to air is calculated by di-

viding the molar mass of the of the gas by 28.9625, the calcu-lated average molar mass of air. See ref. 34 for the averagecomposition of dry air. The specific volume of an ideal gas iscalculated from the ideal gas equation. The volume ratio is:V(ideal gas)/V(liquid in vacuum).

J. The liquid value is not rigorously CP, but rather it is the heatcapacity along the saturation line CS defined by: CS = CP – T(∂V/∂T)P(∂P/∂T)S. For liquids far from the critical point, CS ≈CP.

K. The heating value is the negative of the enthalpy of combustionat 15°C and 101.3250 kPa (abs.) in an ideal reaction (one whereall gasses are ideal gasses). For an arbitrary organic com-pound, the combustion reaction is: CnHmOhSjNk (s,l,or,g) + (n + m/4 – h/2 + j) O2(g) → n CO2(g) + m/2 H2O (g or l) + k/2 N2(g) + j SO2(g), where s, l and g denote respectively solid, liquid and ideal gas.For gross heating values, the water formed is liquid; for netheating values, the water formed is ideal gas. Values reportedare on a dry basis. To account for water in the heating value,see GPA 2172. The MJ/kg liquid column assumes a reactionwith the fuel in the liquid state, while the MJ/m3 ideal gascolumn assumes the gas in the ideal gas state. Therefore, thevalues are not consistent if used in the same calculation, e.g. agas plant balance.

L. The heat of vaporization is the enthalpy of the saturated vaporat the boiling point at 101.3250 kPa minus the enthalpy of thesaturated liquid at the same conditions.

M. Air required for the combustion of ideal gas for compounds offormula CnHmOhSjNk is: V(air)/V(gas) = (n + m/4 - h/2 + j)/0.20946.

COMMENTS

Units: reported values are in SI units based on the following: mass: kilogram, kg length: meter, m temperature: International Temperature of 1990(ITS-90), where 0°C = 273.15 K.

Other derived units are:volume: cubic meter, m3 pressure: Pascal, Pa (1 Pa = N/m2) energy: Joule, J

Gas constant, R: 8.314510 J/(K•mol) 0.008314510 m3(kPa/(K•mol)

1.987216 calth/(K•mol) 1.985887 Btu(I.T.)/(R(lb•mol)

Conversion factors: 1 m3 = 35.31467 ft3 = 264.1721 gal.(U.S.)1 kg = 2.204623 lbm1 kg/m3 = 0.06242795 lbm/ft3 =0.001 g/cm3

1 kPa = 0.01 bar = 0.009869233 atm = 0.1450377 psia 1 atm = 101.3250 kPa = 14.69595 psia = 760 Torr1 kJ = 0.2390057 kcalth = 0.2388459 kcal (I.T.) = 0.9478172 Btu (I.T.)

FIG. 23-2 (Cont’d)

Notes for the Table of Physical Constants

Revised (5-99)23-8

1. Ambrose, D., National Physical Laboratory, Teddington, Middlesex, England: Feb. 1980, NPL Report Chem 107.

2. Ambrose, D.; Hall, D. J.; Lee, D. A.; Lewis, G. B.; Mash, C. J.,J. Chem. Thermo., 11, 1089 (1979).

3. Angus, S.; Armstrong, B.; de Reuck, K. M., Eds. "Carbon Diox-ide. International Thermodynamic Tables of the Fluid State-3,"Pergamon Press: Oxford, 1976.

4. Angus, S.; Armstrong, B.; de Reuck, K. M., Eds. "Methane. In-ternational Thermodynamic Tables of the Fluid State-5," Per-gamon Press: Oxford, 1978.

5. Angus, S.; Armstrong, B.; de Reuck, K. M., "Propylene(Propene). International Thermodynamic Tables of the FluidState-7," Pergamon Press: Oxford, 1980.

6. Angus, S.; de Reuck, K. M.; Armstrong, B., Eds. "Nitrogen. In-ternational Thermodynamic Tables of the Fluid State-6," Per-gamon Press: Oxford, 1979.

7. Angus, S.; de Reuck, K. M.; McCarthy, R. D., Eds. "Helium.International Thermodynamic Tables of the Fluid State-4,"Pergamon Press: Oxford, 1977.

8. Armstrong, G. T.; Jobe, T. L., "Heating Values of Natural Gasand its Components," NBSIR 82-2401, May 1982.

9. Aston, J. G.; Szasz, G. J.; Finke, H. L., J. Am. Chem. Soc., 65,1135 (1943).

10. Barber, C. R., Metrologia 5, 35 (1969).

11. Boundy, R. H.; Boyer, R. F., (Eds.), "Styrene, Its Polymers, Co-polymers and Derivatives," A.C.S. monograph No. 115, Rein-holt, N.Y., 1952.

12. Chaiyavech, P.; Van Winkle, M., J. Chem. Eng. Data, 4, 53(1959).

13. Chao, J.; Hall, K. R.; Yao, J., Thermochimica Acta, 64, 285(1983).

14. CODATA Task Group on Key Values for Thermodynamics, CO-DATA Special Report No. 7, 1978.

15. Commission on Atomic Weights and Isotopic Abundances, Pureand Appl. Chem. 63, 975 (1991).

16. Dean, J. W., "A Tabulation of the Properties of Normal Hydro-gen from Low Temperature to 300 K and from 1 to 100 Atmos-pheres," NBS Tech. Note 120, November 1961.

17. Douslin, D. R.; Huffman, H. M., J. Am. Chem. Soc., 68, 1704(1946).

18. Edwards, D. G., "The Vapor Pressure of 30 Inorganic LiquidsBetween One Atmosphere and the Critical Point," Univ. ofCalif., Lawrence Radiation Laboratory, UCRL-7167. June 13,1963.

19. Engineering Sciences Data Unit, "EDSU, Engineering Sci-ences Data," EDSU International Ltd., London.

20. Flebbe, J. L.; Barclay, D. A.; Manley, D. B., J. Chem. Eng. Data,27, 405 (1982).

21. Francis, A. W., J. Chem. Eng. Data, 5, 534 (1960).

22. Ginnings, D. C.; Furukawa, G. T., J. Am. Chem. Soc. 75, 522(1953).

23. Girard, G., "Recommended Reference Materials of the Realiza-tion of Physicochemical Properties," Chapter 2, Marsh, K. N.Ed.; Blackwell Sci. Pub.: London, 1987.

24. Glasgow, A. R.; Murphy, E. T.; Willingham, C. B.; Rossini, F. D.,J. Res. NBS, 37, 141 (1946).

25. Goodwin, R. D., "Hydrogen Sulfide Provisional Thermochemi-cal Properties from 188 to 700 K at Pressures to 75 MPa,"NBSIR 83-1694, October 1983.

26. Goodwin, R. D.; Haynes, W. M., "Thermophysical Properties ofIsobutane from 114 to 700 K at Pressures to 70 MPa," NBSTech. Note 1051, January 1982.

27. Goodwin, R. D.; Haynes, W. M., "Thermophysical Properties ofNormal Butane from 135 to 700 K at Pressures to 70 MPa,"NBS Monograph 169, April 1982.

28. Goodwin, R. D.; Haynes, W. M., "Thermophysical Properties ofPropane from 85 to 700 K at Pressures to 70 MPa," NBS Mono-graph 170, April 1982.

29. Goodwin, R. D.; Roder, H. M.; Straty, G. C.; "ThermophysicalProperties of Ethane, 90 to 600 K at Pressures to 700 bar," NBSTech. Note 684, August 1976.

30. Guthrie, G. B.; Huffman, H. M., J. Am. Chem. Soc., 65, 1139(1943).

31. Haar, L.; Gallagher, J. S.; Kell, G. S., "NBS/NRC Steam Tables,"Hemisphere Publishing Corporation, Washington, 1984.

32. Huffman, H. M.; Park, G. S.; Thomas, S. B., J. Am. Chem. Soc.,52, 3241 (1930).

33. Hust, J. G.; Stewart, R. B., "Thermodynamic Property Valuesfor Gaseous and Liquid Carbon Monoxide from 70 to 300 At-mospheres," NBS Technical Note 202, Nov. 1963.

34. Jones, F. E., J. Res. NBS, 83, 419 (1978).

35. Keenan, J. H.; Chao, J.; Kaye, J. "Gas Tables: (SI Units)," JohnWiley and Sons, Inc.: New York, 1983.

36. "The Matheson Unabridged Gas Data Book," Matheson GasProducts; New York, 1974.

37. McCarty, R. D.; Weber, L. A., "Thermophysical Properties ofOxygen from the Freezing Liquid Line to 600 R for Pressuresto 5000 Psia," NBS Technical Note 384, July 1971.

38. Messerly, J. F.; Guthrie, G. B.; Todd, S. S.; Finke, H. L., J. Chem.Eng. Data, 12, 338 (1967).

39. Messerly, J. F.; Todd, S. S.; Guthrie, G. B., J. Chem. Eng. Data,15, 227 (1970).

40. Ohe, S., "Computer Aided Data Book of Vapor Pressure," DataBook Publishing Co., Tokyo, Japan, 1976.

41. Roder, H. M., "Measurements of the Specific Heats, Cs, and Cv,of Dense Gaseous and Liquid Ethane," J. Res. Nat. Bur. Stand.(U.S.) 80A, 739 (1976).

42. Scott, R. B.; Meyers, C. H.; Rands, R. D.; Brickwedde, F. G.;Bekkedahl, N., J. Res. NBS, 35, 39 (1945).

43. Stull, D. R.; Westrum, E. F.; Sinke, G. C., "The Chemical Ther-modynamics of Organic Compounds," John Wiley & Sons, Inc.,New York, 1969.

44. "TRC Thermodynamic Tables (Hydrocarbons)," Thermody-namics Research Center, Texas A&M University System: Col-lege Station, Texas.

45. "TRC Thermodynamic Tables (Non-Hydrocarbons)," Thermo-dynamics Research Center, Texas A&M University System:College Station, Texas.

46. Vargaftik, N. B.; "Tables on the Thermophysical Properties ofLiquids and Gases," Hemisphere Publishing Corporation,Washington D.C., 1975.

47. Weast, R. C., "Handbook of Chemistry and Physics," TheChemical Rubber Co: Cleveland, Ohio, 1969.

FIG. 23-2 (Cont ’d)

References for the Table of Physical Constants

23-9

The table in Fig. 23-2 is followed by procedures for estimat-ing compressibility for gases. Additional material follows onhydrocarbon fluid densities, boiling points, ASTM distillation,critical properties, acentric factors, vapor pressures, viscosity,thermal conductivity, surface tension and gross heating value.

COMPUTER PREDICTION METHODS

Computer methods for predicting physical and thermody-namic properties for light hydrocarbons and natural gas con-stituents are widely available. They are routinely used bymany involved in the design and operation of natural gas proc-essing facilities. This section emphasizes hand calculationmethods that give reliable estimates of physical properties.They should be used when a number is required quickly, foran "order of magnitude" check when evaluating a more de-tailed procedure, or when a computer is not available.

There will be presentation of some computer results. Theuse of equations of state for property predictions is convenientand easy, but they do not apply equally well for all properties.Gas phase densities, volumes and compressibilities are pre-dicted accurately and reliably. Liquid volumes and densitiesare less accurate but still can be expected to generally be asreliable as predictions by hand methods. Thermal conductivi-ties, viscosities and surface tensions are not well predicted byPVT equations of state. Computer programs cited or used areselected examples of those widely available for prediction ofphysical and thermodynamic properties. Inclusion here doesnot represent GPA and/or GPSA endorsement of the pro-gram(s). A good, reliable equation of state properly pro-grammed and applied will always be the most convenientmethod for obtaining engineering accuracy gas phase proper-ties. Unfortunately, widespread availability and/or ease of useare not suitable criteria for choice of an equation of state pro-gram. The methods detailed here are for hand calculation ofphysical properties.

Component

MoleFraction,

yi

ComponentCritical

Temperature,Tci, K

ComponentCritical

Pressure,Pci, kPa

Methane 0.8319 190.6 4599

Ethane 0.0848 305.4 4880

Propane 0.0437 369.8 4240

i-Butane 0.0076 407.8 3640

n-Butane 0.0168 425.1 3784

i-Pentane 0.0057 460.4 3381

n-Pentane 0.0032 469.6 3365

n-Hexane 0.0063 507.5 3012

1.0000

G = 20.246/2

FIG

Calculation of Pseudoc ritical Temperature, Pressure

23

COMPRESSIBILITY OF GASES

Pure GasesWhen dealing with gases at very low pressure, the ideal gas

relationship is a convenient and generally satisfactory tool.For measurements and calculations for gases at elevated pre-sure, the use of the ideal gas relationship may lead to errorsas great as 500%, as compared to errors of 2 or 3% at atmos-pheric pressure.

The many PVT equations of state that have been proposed(see Section 25) for representing the pressure-volume-tem-perature relationship of gases are complicated and require acomputer or programmable calculator to solve in a reasonablelength of time. A generalized corresponding states correlationof compressibility factors is reasonably convenient and suffi-ciently accurate for normal engineering requirements. Theprocedure provides a correction factor, Z, by which the volumecomputed from the ideal gas equation is converted to the cor-rect volume for the real gas.

PV = ZmRT / MW = ZnRT Eq 23-1

The compressibility factor Z is a dimensionless parameterindependent of the quantity of gas and determined by thecharacteristics of the gas, the temperature, and pressure.Once Z is known or determined, the calculation of pressure-volume-temperature relationships may be made with as muchease at high pressure as at low pressure.

The equation used to calculate gas density is:

ρ = MW • P8.3145 • T • Z

Eq 23-2

The value 8.3145 for R is used when pressure is in kPa (abs),volume in cubic meters, quantity of gas in kg moles, and tem-perature in K. Values of R for other combinations of units aregiven in Section 1.

According to the theorem of corresponding states, the devia-tion of any actual gas from the ideal gas law is proportionallythe same for different gases when at the same correspondingstate. The same corresponding states are found at the samefraction of the absolute critical temperature and pressure,which, for pure gases, are known as the "reduced conditions."

ComponentMolecular

Mass, MWi

PseudocriticalTemperature

yi•Tci, K

PseudocriticalPressure

yi•Pci, kPa

MixtureMolecular

Massyi • MWi

16.043 158.560 3825.908 13.346

30.070 25.898 413.824 2.550

44.097 16.160 185.288 1.927

58.123 3.099 27.664 0.442

58.123 7.142 63.571 0.976

72.150 2.624 19.272 0.411

72.150 1.503 10.768 0.231

86.177 3.197 19.976 0.543

218.184 = Tc 4565.271 = Pc 20.426 = MW

8.9625 = 0.705

. 23-3

and Average Molecular Mass for a Natural Gas Mixture

-10

Reduced Temperature, Tr = T/Tc Eq 23-3

Reduced Pressure, Pr = P/Pc Eq 23-4

For gas mixtures, the reduced conditions are determined us-ing pseudocritical values instead of the true criticals:

Reduced Temperature, Tr = T/Σ(yiTci) = T/Tpc Eq 23-3a

Reduced Pressure, Pr = P/Σ(yiPci) = P/Ppc Eq 23-4a

Any units of temperature or pressure may be used to deter-mine reduced conditions provided that the same absoluteunits are used for T as for Tc (Tpc) and for P as for Pc (Ppc).The"average molecular weight" for a gas mixture is defined thesame way – MWavg = Σ(yi • MWi). Calculation of pseudo criti-cals and MWavg for a typical natural gas is illustrated in Fig.23-3. Critical temperature and pressure for the hexanes andheavier or heptanes and heavier fraction can be estimatedfrom molecular mass and relative density or average boilingpoint and relative density using procedures presented in thissection.

Attempts to prepare a generalized plot suitable for applica-tion to the low molecular mass hydrocarbons, including meth-ane, ethane, and propane, indicate that an error frequently inexcess of 2 to 3% was unavoidable due to their departure fromthe theorem of corresponding states. Fig. 23-4, prepared usingpure component and gas mixture data, can be used to estimateZ (2-3% error) for pure hydrocarbon gases for this application.Reduced temperature and pressure are used instead ofpseudoreduced values. At low pressures, the different com-pounds appear to conform more closely. The compressibilityfactor may be assumed equal to 1.0 at low pressure. Errorsgenerally will be 2-3% for pressures of 200 kPa (abs) or less solong as the gas is 10°C or more above its saturation tempera-ture at the pressure of concern.

P-H diagrams like those in Section 24, ThermodynamicProperties, can be used to determine gas volumes, densitiesand compressibilities for pure hydrocarbon and nonhydrocar-bon vapors. Interpolation between specific volume curves ona P-H diagram does not yield results of high accuracy. Purecomponent PVT properties are more accurately obtained froman equation of state, particularly if that equation has beenfitted to volumetric data for the specific component. Tabula-tions of properties obtained in this way can be found in theliterature.12

Example 23-1 — Pure component properties

Using Fig. 24-25, the P-H diagram for propane, calculate thedensity of propane vapor at 110°C and 2000 kPa (abs).

Solution

On the P-H diagram at the intersection of the T = 110°C,P = 2000 kPa (abs) lines read v = 0.03 m3/kg. Then:

ρ = 1/0.03 = 33.33 kg/m3

Using the EZ*THERMO90 version of the SRK91 equation ofstate, ρ is calculated to be 32.83 kg/m3, from which v = (1/32.83)= 0.03 m3/kg.

For propane at 110°C and 2000 kPa (abs) using data fromFig. 24-25:

Z = MW • PR • T • ρ

= (44.10) (2000)

(8.3145) (273 + 110) (33.33) = 0.831

The SRK calculation gives ρ = 32.93 kg/m3, and Z = 0.842.

23

Gas MixturesAdditional information regarding the calculation of com-

pressibility factors for mixtures at pressures below1000 kPa (abs) can be obtained from GPA Standard 2172,"Calculation of Gross Heating Value, Relative Density andCompressibility Factor for Natural Gas Mixtures from Com-positional Analysis."

Minor Amounts of Nonhydrocarbons — Fig. 23-41

shows compressibility factors for typical sweet natural gases.Use of compressibility factors from Fig. 23-4 should yield mixturevolumes (densities) within 2 to 3% of the true values from a re-duced temperature slightly greater than 1.0 to the limits of thechart for both temperature and pressure. The chart was preparedfrom data for binary mixtures of methane with ethane, propaneand butane and data for natural gases. No mixtures having av-erage molecular weights greater than 40 were used, and all gasescontained less than 10% nitrogen and less than 2% combinedhydrogen sulfide and carbon dioxide. Fig. 23-4 is applicable fortemperatures 10°C or more above saturation and to pressures ashigh as 70 000 kPa.

Appreciable Amount of Nonhydrocarbons —Fig. 23-4 does not apply for gases or vapors with more than2% H2S and/or CO2 or more than 10% nitrogen. For gas orvapors that have compositions atypical of natural gases, or formixtures containing significant amounts of water and/or acidgases, and for all mixtures as saturated fluids, other methodsshould be employed.

Reasonably accurate gas compressibility factors for naturalgases with high nitrogen content, up to 50% nitrogen or evenhigher, can be obtained using Fig. 23-4 if the molar averagepseudocriticals from Eqs 23-3a and 23-4a are employed. Thissame approach is recommended for gas condensate fluids con-taining appreciable amounts of heptanes and heavier compo-nents. Critical temperature and pressure for the heptane andheavier fraction or fractions can be estimated from molecularmass and relative density, or average boiling point and rela-tive density, using correlations presented in this section.

Figs. 23-5, 23-6 and 23-7 provide compressibility factors forlow molecular mass natural gases. These figures cover a widerange of molecular masses (15.95 to 26.10), temperatures (–70to 500°C), and pressures [up to 35 000 kPa (abs)]. For gaseswith molecular masses between the molecular masses shownin Figs. 23-5 through 23-7, linear interpolation between adja-cent charts should be used to compute the compressibility.

In general, compressibilities for gases with less than 5%noncondensable hydrocarbons, such as nitrogen, carbon diox-ide, and hydrogen sulfide, are predicted with less than 2% er-ror. When molecular mass is above 20 and compressibility isbelow 0.6, errors as large as 10% may occur.

Effect of Acid Gas Content — Natural gases that con-tain H2S and/or CO2 exhibit different compressibility factorbehavior than do sweet gases. Wichert and Aziz3 present acalculational procedure to account for these differences. Themethod uses the standard gas compressibility factor chart(Fig. 23-4) and provides accurate sour gas compressibilities forgas compositions that contain as much as 85% total acid gas.Wichert and Aziz define a "critical temperature adjustmentfactor," ε, that is a function of the concentrations of CO2 andH2S in the sour gas. This correction factor is used to adjust thepseudocritical temperature and pressure of the sour gases ac-cording to the equations:

Tc′ = Tc − ε Eq 23-5

-11

FIG. 23-4

Compressibility Factors for Natural Gas 1

23-12

FIG. 23-5

Compressibility of Low-Molecular-Weight Natural Gases 11

23-13

FIG. 23-6

Compressibility of Low-Molecular-Weight Natural Gases 11

23-14

FIG. 23-7

Compressibility of Low-Molecular-Weight Natural Gases 11

23-15

FIG. 23-8

Pseudocr itical Temperature Adjustment Factor3, ε, °C

Pc′ = Pc Tc′

Tc + B′ (1 − B′)ε Eq 23-6

The pseudocritical temperature adjustment factor is plottedin Fig. 23-8. To use the factor, the pseudocritical temperatureand pressure are calculated following the procedure outlinedearlier. In this calculation, the H2S and CO2 are included aswell as hydrocarbon and other nonhydrocarbon constituents.The pseudocritical temperature adjustment factor is readfrom Fig. 23-8, and used to adjust the values of critical tem-perature and pressure. The reduced temperature and reducedpressure are calculated using the adjusted values. The com-pressibility factor is then read from Fig. 23-4.

Example 23-2 — A sour natural gas has the compositionshown below. Determine the compressibility factor for the gasat 38°C and 6900 kPa (abs).

Solution Steps

The first step is to calculate the pseudocritical temperatureand pseudocritical pressure for the sour gas.

Comp.Mole

FractionCriticalTemp.

Critical Press. yi (Tci) yi (Pci)

CO2 0.10 304.1 7374 30.41 737.40H2S 0.20 373.4 8963 74.68 1792.60N2 0.05 126.2 3398 6.31 169.90CH4 0.60 190.6 4599 114.36 2759.40C2H6 0.05 305.4 4880 15.27 244.00

241.03 5703.30

The pseudocritical temperature adjustment factor is readfrom Fig. 23-8 to be 16.6°C. The adjusted pseudocritical tem-perature is:

Tc′ = 241.03 − 16.6 = 224.43 K

23

The adjusted pseudocritical pressure is:

Pc′ = (5703.3) (224.43)

241.03 + 0.2 (1 − 0.2) 16.6 = 5253 kPa (abs)

The pseudoreduced temperature and pseudoreduced pres-sure are:

Tr = 38 + 273.15

224.43 = 1.39 Pr = 6900

5253 = 1.314

Z = 0.840 (Fig. 23-4)

(The EZ*THERMO90 version of the SRK gives Z = 0.837)

HYDROCARBON LIQUID DENSITIES

Data and CorrelationsFig. 23-9 presents saturated fluid densities (liquid and va-

por) for hydrocarbons and liquid densities for some mixtures.Fig. 23-10 is a plot of relative density as a function of tempera-ture for petroleum fractions.

Subcooled liquid hydrocarbon densities from –20°C to +60°Care shown in Fig. 23-11. Corrections to liquid hydrocarbondensities due to high pressure are shown in Fig. 23-15.

Relative densities of petroleum fractions are given in Fig. 23-12where temperature ranges from 0° to 550°C and pressuresfrom atmospheric to 10 000 kPa (abs). The petroleum fractionis identified within the center grid by two of three charac-teristics — API gravity at 15.5°C, the Watson characterizationfactor, Kw, or the mean-average boiling point. The mean-av-erage boiling point can be determined from Fig. 23-18 togetherwith the API gravity and an ASTM D-86 distillation of the

-16

FIG. 23-9

Hydrocarbon Fluid Densities 2, 3, 19

23-17

FIG. 23-10

Approximate Relative Density of Petroleum Fractions

23-18

FIG. 23-11

Effect of Temperature on Hydrocarbon Liquid Densities 19

23-19

FIG. 23-12

Relative Den sity of Petroleu m Fractions

FIG. 23-13

Relative Densi ty of Pa raffinic Hyd rocarbon Mixtures

petroleum fraction. The characterization factor, Kw, is definedin the inset example shown to illustrate use of Fig. 23-12.

The relative density of paraffinic hydrocarbons at their boil-ing point or bubble point pressure and temperature can beobtained from Fig. 23-13. The nomograph applies to mixturesas well as to single components. Alignment points for paraf-finic mixtures and pure components are located according tomolecular mass. Fig. 23-13 generally predicts specific gravi-ties within 3% of measured values for paraffinic mixtures.However, the accuracy is somewhat less for mixtures having:

• Reduced temperatures above 0.9.• Molecular masses less than 30 (low temperature region)

and where methane is a significant part of the liquid.

Density of Saturated and Subcooled Liquid Mix-tures — A versatile, manual procedure for calculating thedensity of gas-saturated and subcooled hydrocarbon liquidmixtures was presented by Standing and Katz.1 The basicmethod proposed uses the additive volume approach for pro-

23

pane and heavier components at standard conditions, thencorrecting this ideal volume using apparent densities for thegaseous components ethane and methane. The resultingpseudodensity at 15°C and 101.325 kPa (abs) is corrected forpressure using a hydrocarbon liquid compressibility chart(Fig. 23-15), then for temperature using a thermal expansionchart (Fig. 23-17) for hydrocarbon liquids. Experience withcrude oils and rich absorber oils shows this correlation willpredict densities within 1 to 4% of experimental data.

The original correlation did not have a procedure for han-dling significant amounts of nonhydrocarbons and had a fairlynarrow temperature range of 15°C to 115°C. The following pro-cedures and charts are recommended for general applicabilityto liquids containing components heavier than pentanes (gassaturated or subcooled) at pressures up to 70 000 kPa (abs)and temperatures from –80°C to 320°C. Significant amountsof nonhydrocarbons can be handled by this procedure (up to20% N2, 80% CO2, and 30% H2S).

-20

FIG. 23-14

Pseudo Liquid Density of Systems Containing Methane and Ethane

23-21

FIG. 23-15

Density Correction for Compressibi lity of Hy drocarbon Liquids

1. Set up a calculation table as shown in the following ex-ample.

2. Calculate the density of propane and heavier (C3 plus)or, if H2S is present, of H2S and heavier (H2S plus) com-ponents, assuming additive volumes.

Density of C3 plus (or H2s plus)

= Weight C3 plus (or H2S plus) components

Vol C3 plus (or H2S plus) componentsEq 23-7

3. Determine the weight percent of (N2 + C2) in the (N2 + C2 plus) fraction.

Wt % (N2 + C2) = Wt (N2 + C2)

Wt (N2 + C2 plus) • 100 Eq 23-8

4. Use Fig. 23-14 to determine the pseudodensity of the(N2 + C2 plus) fraction. Enter with the C3 plus (or H2Splus) density from Step 2 in the upper left of the chartand go horizontally to the line (interpolate if necessary)representing the weight % (N2 + C2) , then look up andread the pseudodensity of the (N2 + C2 plus) along the topof the chart.

At temperatures below –18°C, ethane can be included inStep 2 and only N2 used in Steps 3 and 4.

5. If CO2 is not present, go to Step 6. If it is present, thenaccount for it on an additive volume basis as shown.

Density of CO2 and (N2 + CO2 plus)

= Wt CO2 + Wt (N2 + C2 plus)Vol CO2 + Vol (N2 + C2 plus)

Eq 23-9

where

23

Vol (N2 + C2 plus) = Wt (N2 + C2 plus)

Density (N2 + C2 plus)

6. Calculate the weight percent methane,

Wt % methane = Wt methane

total Wt • 100 Eq 23-10

7. Enter the top of Fig. 23-14 with the pseudodensity fromStep 4 or 5 as appropriate, and drop vertically to the line(interpolation may be required) representing the weightpercent methane. Read the pseudodensity of the mixture[15°C and 101.325 kPa (abs)] on the right side of thechart.

8. Correct the pseudodensity to the actual pressure usingFig. 23-15. Add the correction to the pseudodensity fromStep 7.

9. Correct the density at 15°C and pressure to the actualtemperature using Fig. 23-16. Add the correction to thedensity from Step 8.

This procedure should not be used in the critical region. Mix-tures at temperatures greater than 65°C that contain morethan 60 mole percent methane or more than 80 mole percentCO2 have been demonstrated to be problem areas. Away fromthe near critical region calculated densities usually are within5% of experimental data and errors are rarely greater than8%. The best accuracy is obtained for mixtures containingmostly C5 plus with relatively small amounts of dissolvedgaseous components (errors are usually less than 3%). Notethat densities of C2 plus, C3 plus, CO2 plus, or C4 plus mixturescan be calculated by this procedure at various temperaturesand pressures, and that the gaseous components need not bepresent.

-22

(1) (2) (3) (4) (5) (6)=(4)/(5)

Component MoleFraction

MolecularMass Mass, kg Density (15°C),

kg/m3 Volume, m3

Methane 0.20896 16.043 3.352 – –Carbon Dioxide 0.39730 44.010 17.485 821.94 0.02127Ethane 0.01886 30.070 0.567 – –Propane 0.02387 44.097 1.053 507.30 0.00207n-Butane 0.03586 58.123 2.084 584.06 0.00357n-Pentane 0.02447 72.150 1.766 631.00 0.00280n-Hexane 0.01844 86.177 1.589 663.89 0.00239n-Heptane 0.02983 100.204 2.989 687.84 0.00435n-Octane 0.02995 114.231 3.421 706.54 0.00484n-Decane 0.18208 142.285 25.907 733.86 0.03530n-Tetradecane 0.03038 198.394 6.027 765.90 0.00787Total 1.00000 66.240Mass C3 plus 44.83626684Vol C3 plus 0.063195095132604Density C3 plus 709.48966444182Mass% C2 0.012490702499802Mass CO2 plus 62.88856004Vol CO2 plus 0.084468147910179Den CO2 plus 744.52396075825Mass% CH4 0.050608385616189

FIG. 23-16

Calculation o f Liquid Dens ity of a Mixture at 50°C and 12 000 kPa (abs)

Example 23-3 — Fig. 23-16 illustrates the procedure outlinedabove to calculate necessary numbers for the following exam-ple.

Density of C3 plus = Wt of C3 plusVol of C3 plus

= 44.836 kg0.0632 m3

= 709.5 kg/m3

Mass % C2 in C2 plus = 0.5670.567 + 44.836

• 100 = 1.25%

Density of C2 plus from Fig. 23-14 = 705 kg/m3

Density of CO2 plus = 62.889 kg0.0845 m3 = 744.52 kg/m3

Mass % CH4 in Total = 3.35266.241

• 100 = 5.1%

Pseudodensity of mixture at 15°C and 101.325 kPa (abs) fromFig. 23-14 = 680 kg/m3

Pressure correction to 12 000 kPa (abs) from Fig. 23-15 = 12.5

Density at 15°C and 12 000 kPa (abs) = 680 + 12.5

= 692.5 kg/m3

Temperature correction to 50°C from Fig. 23-17 = –30

Density at 50°C and 12 000 kPa (abs) = 692.5 − 30

= 662.5 kg/m3

23

(Density by EZ*THERMO version of SRK using Costald92

668 kg/m3.

Experimental density35 at 50°C and 12 000 kPa (abs) = 660 kg/m3

Error = (662.5 − 660)/660 = 0.0038 = 0.38%

BOILING POINTS, CRITICALPROPERTIES, ACENTRIC FACTOR,

VAPOR PRESSURE

Boiling PointsFig. 23-18 shows the interconversion between ASTM D-86

distillation 10% to 90% slope and the different boiling pointsused in characterizing fractions of crude oil to determine theproperties; VABP, WABP, CABP, MeABP, and MABP. On thebasis of ASTM D-86 distillation data, the volumetric averageboiling (VABP) point is defined as:

VABP = (t10 + t30 + t50 + t70 + t90)/5 Eq 23-11

Where the subscripts 10, 30, 50, 70, and 90 refer to thevolume percent recovered during the distillation. The 10%to 90% slope used as the abscissa in Fig. 23-18 is defined as:

slope = (t90 − t10)/(90 − 10) Eq 23-12

To use the graph, locate the curve for the distillation VABPin the appropriate set for the type of boiling point desired. Forthe known 10-90% slope calculated by Eq. 23-12, read a cor-rection for the VABP from the selected VABP curve.

-23

FIG. 23-17

Density Correction for Thermal Expansion of Hydrocarbon Liquids

23-24

FIG. 23-18

Characterized Boiling Points of P etroleum Fraction s (From API Technical Data Boo k)

Example 23-4 — Determine the mean average boiling point(MeABP) and the molecular mass for a 56.8° API petroleumfraction with the following ASTM D-86 distillation data.

% Over Temperature, °CIBP 37.8

5 54.410 67.220 88.330 102.840 117.850 137.860 159.470 195.680 240.090 311.1EP 337.8

IBP = initial boiling point, EP = end point

Slope = (311.1 − 67.2)/80 = 3.05

VABP = (67.2 + 102.8 + 137.8 + 195.6 + 311.1)/5 = 162.9°C

Refer to Fig. 23-18. Read down from a slope of 3.05 to theinterpolated curve for 162.9°C in the set drawn with dashedlines (MeABP). Read a correlation value of –29.5 on the ordi-nate. Then:

MeABP = 162.9 − 29.5 = 133.4°C

23

A discussion of the significance of the various average boil-ing points, interconversion of D-86 and D-1160 ASTM distilla-tions, and the calculation of true-boiling point andatmospheric flash curves from ASTM distillation data can befound in Chapters 3 and 4 of the API Technical Data Book.36

Molecular mass can be calculated from Eq 23-13 using MeABPin K, and S (relative density at 15°C) .

MW = 204.38 (1.8 • T)0.118

S

1.88

e

(0.00392 T − 3.075 S

Eq 23-13

This relationship has been evaluated in the molecular massrange of 70 to 720; the MeABP of 36 to 560°C; and the APIrange of 14° to 93°. Its average error was about 7%. Eq. 23-13is best used for molecular masses above 115, since it tends toover-predict below this value.

Example 23-5 — Calculation of molecular mass.

From Example 23-4:

S = 0.7515 for 56.8° API

MeABP = 133.4 + 273 = 406.4 K

Using Eq 23-13,

MW = 204.38[(1.8 • 406.4)0.118]

[(0.7515)1.88] e(0.00392 • 406.4) − (3.075 • 0.7515) = 127.0

-25

FIG. 23-19

Low-Temperature Vapor Pressures for Light Hydrocarbons

23-26

FIG. 23-20

High-Temperature Vapor Pressures for Light Hydrocarbons

23-27

FIG. 23-21

Viscosities of Hydrocarbon Liquids

FIG. 23-22

Viscosity of Paraffin Hydrocarbon Gases at One Atmosphere

23-28

FIG. 23-23

Hydrocarbon Gas Viscosity

Courtesy Western Supply Co., Tulsa

Revised (5-99)23-29

Critical PropertiesCritical properties are of interest because they are com-

monly used to find reduced conditions of temperature andpressure which are required for corresponding states correla-tions. Pseudocriticals are used in many corresponding statescorrelations for mixtures.

The following equations taken from the API Technical DataBook36a, b can be used to estimate pseudo critical temperatureand pressure for petroleum fractions (pseudo, or undefinedcomponents):

Ppc = 5.5303 199 T

−2.3125 • S 2.3201 Eq 23-14

Tpc = 19.0623 • T0.58848 • S0.3596 Eq 23-15

These equations are in terms of T = MeABP ( K) andrelative density (S) at 15°C. Both of these correlationshave been evaluated over the range of 80 to 690 molecularmass; 20 to 150°C normal boiling point; and 6.6° to 95°API.Example 23-6 — Pseudocritical temperature and pressure.

Take the previous mixture (from Example 23-4) with:VABP = 166.4°CMeABP = 118.4°CAPI = 56.8°Molecular Weight = 127 (Ex. 23-5)ASTM D-86, 10% to 90% Slope = 3.05

Find its pseudocritical temperature.Solution Steps

From Fig. 23-18 with ASTM D-86 slope = 3.05 find a VABPcorrection of about –65°C (extrapolated from the left-handgroup).

MABP = 166.4 − 65 = 101.4°C

Use Eq 23-15 to calculate the pseudocritical temperatureas:

Tpc = 19.0623 (118.4 + 273)0.58848 (0.7515)0.3596

= 577.1 K = 304.1°CFor this 56.8° API fluid, estimate the pseudocritical pres-

sure, using Eq. 23-14 and MeABP = 118.4°C:

Ppc = [5.5303 (109)] (118.4 + 273)−2.3125 (0.7515)2.3021

= 2865 kPa (abs)

Acentric FactorThe acentric factor, ω, is frequently used as a third parame-

ter in corresponding states correlations. It is tabulated forpure hydrocarbons in Fig. 23-2. Note that the acentric factoris a function of Pvp, Pc, and Tc.

It is arbitrarily defined by

ω = −log (Pvp/Pc) Tr = 0.7 − 1.0 Eq 23-16

This definition requires knowledge of the critical (pseudo-critical) temperature, vapor pressure, and critical (pseudo-critical) pressure.

For a mixture of known composition, and containing similarcomponents, the acentric factor may be estimated, with rea-sonable accuracy, as the molar average of the individual purecomponent acentric factors:

ω = Σ xi ωi Eq 23-17

23

If the vapor pressure is not known, ω can be estimated38 forpure hydrocarbons or fractions with boiling point ranges of10°C or less, using Eq. 23-18.

ω =

37

log Pc − log 14.7

Tc

Tb

− 1

− 1.0 Eq 23-18

Example 23-7 — Acentric factor.A narrow-boiling petroleum fraction has a VABP of 214.4°C,

an ASTM slope of 0.75 and an API gravity of 41°. Estimate itsacentric factor.

In order to use Eq 23-18 we need the average boiling point(MeABP); the pseudocritical temperature (a function of MABP);and the pseudocritical pressure (a function of MeABP).

From Fig. 23-18, the correction to VABP for mean averageis –1.7°C; and the correction for MABP is –2.8°C. Note thatfor narrow-boiling fractions, all boiling points approach thevolumetric average. Then, MeABP = 212.7°C and MABP is211.6°C.

From Eq. 23-14, the pseudocritical pressure is:T = 212.7 + 273.15 = 485.85 K

S for 41° API = 141.5/(131.5 + 41) = 0.871

Ppc = 5.5303 109(485.85)−2.3125

• (0.871)2.3201

Ppc = 2460 kPa (abs)

From Eq. 23-15, the pseudocritical temperature is:

Tpc = 19.0623 • (485.85)0.58848 • (0.871)0.3596

Tpc = 691.2 K

ω =

37

log (2460) − log (101.325 )

691.2485.85

− 1

− 1.0 = 0.505

Vapor PressureThe vapor pressures of light hydrocarbons and some com-

mon non-hydrocarbons in the temperature range below 38°Care given in Fig. 23-19. Vapor pressures at higher tempera-tures, up to 315°C, are given in Fig. 23-20 for the same com-pounds. Note that, except for ethylene and propylene, thehydrocarbons are all normal paraffins.

VISCOSITY

Figs. 23-21 through 23-29 give the viscosity of hydrocarbonliquids and vapors, water, steam, and miscellaneous gases.Fig. 23-21 gives data on hydrocarbon liquids. Figs. 23-22, 23-23 and 23-24 present data on hydrocarbon gases. To correctfor pressure, the gas viscosity from Fig. 23-22 is adjusted fromatmospheric pressure values by Fig. 23-24, or it can be readdirectly from Fig. 23-23. Fig. 23-24 is preferred when the re-duced temperature is greater than 1.0. Fig. 23-28 gives theviscosity of hydrocarbon liquids containing dissolved gases.Note that Fig. 1-7 gives conversion factors for viscosity.

Calculation of Gas Mixture ViscosityExample 23-8—Determine the viscosity of a gas of molecu-lar mass 22 at 6895 kPa (abs) and 40°C. Tc = 226.9 K, Pc = 4885 kPa(abs).

Revised (5-99)-30

FIG. 23-25

Viscosity of Miscellaneous Gases – 101 kPa (abs)

FIG. 23-26

Viscosity of Air 43, 44, 45

FIG. 23-24

Viscosity Ratio For Natural Gases

23-31

FIG. 23-27

Water Viscosity at Saturated Conditions

Solution Steps

Gid = 22/28.9625 = 0.760

From Fig. 23-22 at 40°C:

µA = 0.0105 mPa • s

Then:

Tr =

40 + 273226.9

= 1.38 Pr =

68954885

= 1.411

Note: Pseudocritical temperature and pressure should becalculated as outlined in this section, if the composition of thegas is available.

Because Tr > 1.0, Fig. 23-24 is preferred over Fig. 23-23 toobtain the correction for elevated pressure to the viscosity atone atmosphere.From Fig. 23-24:

µµA

= 1.21

Hence, the viscosity at 6895 kPa (abs) and 40°C is:

µ = (1.21) (0.0105) = 0.0127 mPa • s

The viscosity of a gaseous mixture with large amounts ofnonhydrocarbons is best determined by using the methodof Dean and Stiel.41 This method is particularly useful forhandling natural gas with high CO2 content. Tested against30 CO2-N2 mixtures, it had an average deviation of 1.21%at pressures up to 24 300 kPa (abs). It makes use of a factor,ξ, defined as:

ξ = 21.74

(Tcm ) 1/6

Σ (yi MWi ) 1/2 (Pcm )

2/3

Eq 23-20

If the reduced temperature, Tr is > 1.5, then

ξ (µA) = 166.8 (10−5) (0.1338 Tr − 0.0932)5/9

Eq 23-21

If Tr is ≤ 1.5,

ξ (µA) = 34.0 (10−5) (Tr )8/9 Eq 23-22

In either case, µA is found by dividing (ξ µA) by ξ.Equations 23-20 through 23-22 will predict the viscosity of

pure gases as well as mixtures. To apply the Dean and Stielmethod to mixtures, the pseudocritical volumes, compressi-bilities, and temperatures are calculated by the Prausnitz andGunn42 rules:

Vcm = Σ (yi Vci) Eq 23-23

Zcm = Σ (yi Zci) Eq 23-24

Tcm = Σ (yi Tci) Eq 23-25

Pcm =

Zcm R Tcm

Vcm

Eq 23-26

Example 23-9 — For a temperature of 10°C and a pressureof 2000 kPa (abs), estimate the viscosity of a mixture of 80mole percent methane, 15 mole percent nitrogen, and 5 molepercent carbon dioxide. See Fig. 23-30:

23

Pcm = Zcm R Tcm

Vcm

= (0.2871) (8.31) (186.6)

0.0973 = 4581.8 kPa (abs)

Substituting from the calculation table in Fig. 23-30 intoEq 23-20:

ξ = (21.74) (186.6)1/6

(19.237)1/2 (4581.8)2/3 = 0.043

Tr = T

Tcm =

283186.6

= 1.52

Because Tr > 1.5, the expression for ξµA is Eq 23-21.

ξ µA = 166.8 (10−5) (0.1338 Tr − 0.0932)5/9

= 166.8 (10−5)

(0.1338 • 1.52 − 0.0932)5/9

ξ µA = 48.98 10−5

µA = 0.01147 mPa • s

Using Fig. 23-22 and correcting for the nitrogen and carbondioxide content of this mixture gives a µA of 0.0116 cp. This isa good check. Had a 20% N2 content been chosen for this ex-ample, the N2 range of Fig. 23-22 would have been exceededand use of the Dean and Stiel method would have been re-quired. When the conditions at hand fall within the limits ofFig. 23-23, use this figure and not the Dean and Stiel correlation.

Revised (5-99)-32

FIG. 23-28

Liquid Viscosity of Pure and Mixed Hydrocarbons Containing Dissolved Gases at 38°C and 101.325 kPa (abs)

23-33

FIG. 23-29

Viscosity of Steam46, 47

Viscosity of Petroleum Fractions

Mid-Boiling Point Method — The viscosity of a crudeoil or crude oil fraction can be estimated using the equationsgiven below if the mid-boiling point and gravity are known:

Mid-boiling point is defined as the boiling point at 50% vol-ume distilled.

η = A • e B / T Eq 23-27

A = 91.83 Tb − 0.175 − 29.263

Kw

BEq 23-28

ln (B) = 4.717 + 0.00526 Tb Eq 23-29

Example 23-10 — At 40°C and 100°C find the viscosity of aheavy condensate having a mid-boiling point of 163°C anda relative density of 0.7688.

MoleFraction, yi

MolecularMass, MWi

Pci,kPa (abs)

CH4 0.80 16.043 4599 N2 0.15 28.013 3398 CO2 0.05 44.010 2374

Mixture1.00 19.237

—Σ MWcm = Σyi • MWi Tc

FIG.

Calculation of Visco

23

Solution Steps

Kw = 3√ (163 + 273) • 1.8

0.7688 = 11.99

ln (B) = 4.717 + (0.00526) (163 + 273) = 7.01

B = 1108

A = 91.83 (436) − 0.175 − 29.263

11.991108

= 0.02638

The same constants are employed at 40°C and 100°C.

η = 0.02638 • e1108313 = 0.909 cs at 40°C

η = 0.02638 • e1108373 = 0.513 cs at 100°C

The reported values are 0.93 and 0.52 centistokes, respec-tively.

THERMAL CONDUCTIVITY

Thermal conductivity for natural gas mixtures at elevatedpressure can be calculated from an atmospheric value and apressure correction. Figs. 23-31 through 23-34 present lowpressure thermal conductivity data of gases developed frompublished data.51, 54 The pressure correction of Lenoir et al.52

shown in Fig. 23-32 is applied to these low pressure data asillustrated below. The thermal conductivity of liquid paraffinhydrocarbons is plotted in Fig. 23-35 and the thermal conduc-tivity of liquid petroleum fractions in Fig. 23-36.Example 23-11 — Find the thermal conductivity of a 25 molecu-lar mass natural gas at 4826 kPa (abs) and 140°C. Tc = 244 K,Pc = 4550 kPa (abs)

Solution Steps

From Fig. 23-31, at 140°C:

kA = 0.0445 W/(m • °C)

Tr = (140 + 273)/244 = 1.69

Pr = 4826/4550 = 1.06

From Fig. 23-32:

k/kA = 1.13

k = (1.13) (0.0445) = 0.0503 W/(m • °C)Another method for estimating thermal conductivity is pre-

sented by Stiel and Thodos.53

To determine the thermal conductivity of a gaseous mixtureof defined components, the thermal conductivity of each com-ponent at the given temperature is read from the chart pro-vided and the thermal conductivity of the mixture is

Tci, K vci , m3/kg Vci = MWi • vcim3/kg mole Zci =

Pci • Vci

8.31 • Tci

190.56 0.00617 0.0990 0.2875126.21 0.00318 0.0891 0.2887304.11 0.00214 0.0942 0.2749

186.59—

0.0973 0.2871

m = Σyi • Tci Vcm = Σyi • Vci Zcm = Σyi • Zci

23-30

sity of a Gas Mixture

Revised (5-99)-34

FIG. 23-31

Thermal Condu ctivi ty of Natural and Hyd rocarbon Gasesat One Atmosph ere [101.325 kPa (abs)]

FIG. 23-32

Thermal Conduc tivity Ratio for Gases

determined by the "cube root rule."56 This rule is applicableto mixtures of simple gases; it does not apply to mixtures con-taining CO2 because the thermal conductivity goes through amaximum.

km = Σ (yi ki

3√MWi )

Σ yi 3√MWi

Eq 23-30

The cube root rule was tested56 against 17 systems with anaverage deviation of 2.7%.

The thermal conductivity of a liquid mixture is best deter-mined by the method of Li,55 based on volume fractions.

Example 23-12 — Find the thermal conductivity of the gase-ous mixture shown in Fig. 23-37 at 100°C and one atmosphere.

km = 0.107802.822

= 0.0382 W/(m • °C)

TRANSPORT PROPERTY REFERENCES

There are no simple correlations for the transport propertiesof viscosity and thermal conductivity, as evident from the pre-ceding paragraphs. For pure components, the best approachis a complicated equation with many constants that must befitted to experimental data, or extensive tables. Vargaftik62

and Touloukian65 each have extensive collections of experi-mental data.

23

SURFACE TENSION

The interior molecules of a liquid exert upon the surfacemolecules an inward force of attraction which tends to mini-mize the surface area of the liquid. The work required to en-large the surface area by one square centimeter is called thesurface free energy. The perpendicular force in the liquid sur-face, called surface tension, exerts a force parallel to the planeof the surface. Surface tension, an important property wherewetting, foaming, emulsification, and droplet formation areencountered, is used in the design of fractionators, absorbers,two-phase pipelines, and in reservoir calculations.

Pure Components

The surface tension of pure hydrocarbons as a function oftemperature may be obtained from Fig. 23-38.

Mixtures

Surface tension for binaries of known composition at or nearatmospheric pressure may be calculated78 using:

σm = σ1 • σ2

σ1 • x2 + σ2 • x1Eq 23-31

The presence of inert gases, such as N2 and CO2, in the liquidphase tends to lower the surface tension of the liquid. Where theconcentration of inert gases in the liquid exceeds 1.0 mole%, es-timated values of surface tension may be 5 to 20% higher thanactual values for the mixture.

-35

FIG. 23-33

Thermal Cond uctivi ty of Miscellan eous Ga ses at One Atmosp here59, 60, 61, 62

FIG. 23-34

Thermal Condu ctivi ty of Hydrocarbon Gases at One Atmosp here67, 68, 69

GROSS HEATING VALUE OF NATURALGASES

The gross heating value, relative density, and compressibil-ity of a natural gas mixture may be calculated when a completecompositional analysis of the mixture is available.

Gross Heating Value — is defined as the total energytransferred as heat in an ideal combustion reaction at a stand-ard temperature and pressure in which all water formed ap-pears as liquid. The gross heating value can be calculated perunit volume of an ideal gas, or per unit volume of a real gas asfollows:

Hv = Σ yi Hvi

Eq 23-32

Values for Hv and MWi are obtained from Fig. 23-2.

To calculate the ideal gross heating value produced or usedfor a given period of time, Hv must be multiplied by the idealgas volumetric flow rate of gas for the time period. To employa real gas flow to calculate the ideal gross heating value pro-duced or used for a given period of time, the real gas flow ratemust be converted to the ideal gas flow rate by dividing by thecompressibility factor. Often the heating value Hv is dividedby the compressibility factor in preparation for multiplying bythe real gas flow rate. Thus Hv/Z is gross heating value perunit volume of real gas.

Relative Density (also termed specific gravity or gasgravity) — is defined as the ratio of gas density (at the tem-perature and pressure of the gas) to the density of dry air (atthe air temperature and pressure).

23

G = ρρs

= MW P Ta Za

MWa Pa ZEq 23-33

The ideal gas relative density is the ratio of the molecularmass of the gas to the molecular mass of dry air.

Gid = MWMWa

Eq 23-34

For a mixture

G id = Σ yi Gi id

Eq 23-35

The relative density G is measured and is generally used tocalculate the molecular mass ratio Gid when the gas composi-tion is not available.

G id = MWMWa

= G (Pa T Z)

P Ta ZEq 23-36

The temperatures and pressures used must correspond toactual measurement conditions or serious errors in Gid canoccur.

Corrections for Water Content — When the gas iswater saturated but the component analysis is on a dry basis,the component analysis must be adjusted to reflect the pres-ence of water. The mole fraction of water in the mixture isestimated as:

yw = Pw

o

p =

nw

(1 + nw) (on a one mole basis)

-36

FIG. 23-35

Thermal Conductivity of Liquid Paraffin Hydrocarbons

FIG. 23-36

Thermal Conductivity of Liquid Petroleum Fractions 58

23-37

Component MoleFraction

ThermalConductivity

W/(m • °C)Molecular

Mass3√MWi (yi

3√MWi) (yi ki

3√MWi )

CO2 0.10 0.0225 44.010 3.530 0.3530 0.00794

H2S 0.20 0.0240 34.076 3.242 0.6484 0.01556

N2 0.05 0.0310 28.013 3.037 0.1519 0.00474

CH4 0.60 0.0410 16.043 2.522 1.5132 0.07474

C2H6 0.05 0.0310 30.070 3.109 0.1555 0.00482

Total 1.00 2.8220 0.10780

FIG. 23-37

Calculation of Thermal Conductivity

FIG. 23-38

Surface Tension of Paraffin Hydrocarbons 85

23-38

The adjusted mole fractions are calculated using the follow-ing equation:

yiw = yi

1 −

Pwo

P

= yi (1 − yw) Eq 23-37

For water saturated gas, water is added to the componentlist and the xi

w values are used in the gross heating value andthe gas compressibility calculations. If the dry gross heatingvalue is known, the water saturated gross heating value canbe calculated by:

Hv(sat’d) = 1 −

1.7051P

Hv (dry) +

1.7051 • 29.94P

Eq 23-38When the gas is wet but not water saturated and the com-

ponent analysis is on a dry basis, it is necessary to determinethe water content and to adjust the mole fractions to reflectthe presence of water. When the water mole fraction, yw, isknown, the adjusted mole fractions can be obtained from Eq23-37.

The yiw values are used in the gross heating value and gas

compressibility calculations after adding water to the compo-nent list. If the dry gross heating value is known, the effect ofthe water content can be calculated using:

Hv (wet) = (1 − yw) Hv (dry) + 50.3 yw Eq 23-39

Calculations — Additional details on these calculationalmethods and examples are given in GPA Standard 2172, "Calcu-lation of Gross Heating Value, Relative Density and Compressi-bility Factor for Natural Gas Mixtures from CompositionalAnalysis." A listing of the Basic source code for a computerprogram to perform the calculations is given in 2172.

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