SECTION 23

Physical PropertiesThis section contains a number of charts, correlations, and

procedures for the prediction of physical properties of hydro-carbons and components found with them. Fig. 23-1 lists thenomenclature 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-

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.

B = second virial coefficient for a gas mixture,(psia)-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, F

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

Giid = molecular weight ratio of component i in mixture

Hv = gross heating value per unit volume of ideal gas,Btu/cu ft

Kw = Watson characterization factor, Fig. 23-12k = thermal conductivity, Btu/[(hr sq ft F)/ft]

ka = thermal conductivity at one atmosphere,Btu/[(hr sq ft F)/ft]

M = mass fractionm = mass, lb

MW = molecular weight, lb/lb moleMABP = molal average boiling point, F or R

MeABP = Mean average boiling point, F or Rn = number of moles, (mass/Mole weight)P = pressure, psia

Pc = pseudocritical pressure adjusted for acid gascomposition, psia

W = mass, lbWABP = weight average boiling point, F

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

Greek = pseudocritical temperature adjustment factor,

Eq 23-6 = MeABP/Tpc = density, lb/cu ft = viscosity at operating temperature and pressure,

centipoiseA = viscosity at 14.7 psia (1 atm) and operating

temperature, centipoise = factor defined by Eq 23-20 = surface tension, dynes/cm = acentric factor = kinematic viscosity, centistokes

Subscriptsa = airb = boilingc = critical

FIG. 23-1NomenclaturePvp = vapor pressure at a reduced temperature of 0.7Pw

o = vapor pressure of water, 0.25636 psia at 60FR = gas constant, 10.73 (psia cu ft)/(R lb mole) for

all gases (see Section 1 for R in other units)S = specific gravity at 60/60FT = absolute temperature, Rt = ASTM D-86 distillation temperature for a given volumetric fraction, F or R, Eq 23-11Tc = pseudocritical temperature adjusted for acid gas

composition, RV = volume, cu ft

VABP = volumetric average boiling point, F

23i = component iL = liquidm = mixturepc = pseudocritical

r = reduced stateV = vaporv = volume

w = water

Superscriptsid = ideal gasw = water

o = reference state

-1

FIG. 23-2Physical Constants23-2

FIG. 23-2 (Contd)Physical Constants23-3

FIG. 23-2 (Contd)Physical Constants23-4

FIG. 23-2 (Contd)Notes and References for the Table of Physical Constants23-5

FIG. 23-2 (Contd)Notes and References for the Table of Physical Constants23-6

FIG. 23-2 (Contd)Notes and References for the Table of Physical Constants23-7

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 60F. 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 60F 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, 4.540 [29];Propane, 4.484 [28]; Propene, 5.083 [5]; Hydrogen Chloride,9.948 [43]; Hydrogen Sulfide, 7.919 [25]; Ammonia, 5.688 [43];Sulfur Dioxide, 12.20 [43].

u. Technically, water has a heating value in two cases: net (1060.Btu/lb) when water is liquid in the reactants, and gross(+50.313 Btu/ft3) 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 weight) 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 14.696 psia.

C. Freezing point: the temperature at equilibrium between the crys-talline phase and the air saturated liquid at 14.696 psia.

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 (specific gravity): (liquid, 60F)/(water,60F). The density of water at 60F is 8.3372 lb/gal.

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

G. Pitzer acentric factor: = 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 heat ca-pacity 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 60F and 14.696 psia in an ideal reaction (one where allgasses are ideal gasses). For an arbitrary organic compound,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 Btu/lb or gal. liquid column assumes a re-action with the fuel in the liquid state, while the Btu/ft3 idealgas column assumes the gas in the ideal gas state. Therefore,the values are not consistent if used in the same calculation,e.g. a gas plant balance.

L. The heat of vaporization is the enthalpy of the saturated vaporat the boiling point at 14.696 psia 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 based upon the following units withtheir equivalent corresponding SI units: mass: Pound (avdp), lbm = 0.45359237 kglength: foot, ft = 0.3048 m temperature: degree Fahrenheitt/F) = 32 = [1.8(t/C)].The Celsius scale is defined by the International Temperatureof 1990 (ITS-90), where 0C = 273.15 K.

Other derived units are:volume: cubic foot, ft3 = 0.02831685 m3 gallon = 231 in3 = 0.0037854512 m3

pressure: pound per square inch absolute psia = 6894.757 kPa

energy: British thermal unit (I.T.) Btu = 251.9958 cal (I.T.) = 1055.056 J

Gas constant, R:1.985887 Btu (I.T.)/(R lb mol)10.73164 ft3 psia/(R lb mol) 8.314510 J/(K(mol)

Conversion factors: 1 ft3 = 7.480520 gal.1 lbm/ft3 = 0.1336806 lbm/gal = 16.018462 kg/m3

1 psia = 0.06804596 atm = 6.894757 kPa1 atm = 14.69595 psia = 760 Torr = 101.3250 kPa1 Btu (I.T.) = 252.1644 calth

FIG. 23-2 (Contd)Notes for the Table of Physical Constants23-8

FIG. 23-2 (Contd)1. Ambrose, D., National Physical Laboratory, Teddington, Mid-dlesex, 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, Thermodynam-ics Research Center, Texas A&M University System: CollegeStation, Texas.

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

References for the Table of Physical Constants23-9

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 themody-namics 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.

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 pres-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 real gas.

PV = ZmRT /MW = ZnRT Eq 23-1The compressibility factor Z is a dimensionless parameter

.

rThere 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.

ComponentMole

Fraction,yi

ComponentCritical

Temperature,Tci, R

PseudocriticalTemperature,

Tpc, R

CH4 0.8319 343.0 285.3

C2H6 0.0848 549.6 46.6

C3H8 0.0437 665.7 29.1

iC4H10 0.0076 734.1 5.58

nC4H10 0.0168 765.3 12.86

iC5H12 0.0057 828.8 4.72

nC5H12 0.0032 845.5 2.71

nC6H14 0.0063 913.3 5.75

Tpc = 392.62

FIGCalculation of Pseudocritical Temperatu23independent 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-temperature-volume relationships may be made with as muchease at high pressure as at low pressure.

The equation used to calculate gas density is:

= MW P10.73 T Z

Eq 23-2

The value 10.73 for R is used when pressure is in psia, vol-ume in cubic feet, quantity of gas in pound moles, and tem-perature in R. 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 presumably are foundat the same fraction of the absolute critical temperature andpressure, which, for pure gases, are known as the reducedconditions.

ComponentCritical

Pressure,Pci, psia

PseudocriticalPressure,Ppc, psia

ComponentMolecular

Weight, MW

MixtureMolecular

Weight,yi MW

666.4 554.4 16.043 13.346

706.5 59.9 30.070 2.550

616.0 26.9 44.097 1.927

527.9 4.01 58.123 0.442

550.6 9.25 58.123 0.976

490.4 2.80 72.150 0.411

488.6 1.56 72.150 0.231

436.9 2.75 86.177 0.543

Ppc = 661.57 MWm = 20.426

G = 20.426/28.9625 = 0.705

23-3e and Pressure 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/(yiTci) = T/Tpc Eq 23-3aReduced Pressure, Pr = P/(yiPci) = P/Ppc Eq 23-4a

Any units of temperature or pressure may be used providedthat the same absolute units be used for T as for Tc (Tpc) andfor P as for Pc (Ppc). The average molecular weight for a gasmixture is defined the same way MWavg = (yi MWi). Cal-culation of pseudo criticals and MWavg for a typical natural gasis illustrated in Fig. 23-3. Critical temperature and pressurefor the hexanes and heavier or heptanes and heavier fractioncan be estimated from molecular weight and specific gravityor average boiling point and relative density using procedurespresented in this section.

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 300 psia or less so longas the gas is 50F or more above its saturation temperatureat 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 propertiesUsing Fig. 24-26, the P-H diagram for propane, calculate the

density of propane vapor at 200F and 100 psia.

Solution Steps

On the P-H diagram at the intersection of the T = 200F, P = 100 psia lines read v = 1.5 ft3/lb. Then:

= 1/1.5 = 0.667 lb.ft3

Using the EZ*THERMO90 version of the SRK91 equation ofstate, is calculated to be 0.662 lb/ft3, from which v = (1/0.662) = 1.51 ft3/lb.

For propane at 200F and 100 psia using data from Fig.24-26

Z = MW PR T =

(44.10) (100)(10.73) (458.67 + 200) (0.667) = 0.936

The SRK calculation gives = 0.662 lb/ft3, and Z = 0.941.23-Gas MixturesAdditional information regarding the calculation of compressi-

bility factors for mixtures at pressures below 150 psia can beobtained from GPA Standard 2172, Calculation of Gross HeatingValue, Relative Density and Compressibility Factor for NaturalGas Mixtures from Compositional Analysis.

Minor Amounts of Nonhydrocarbons Fig. 23-41shows compressibility factors for typical sweet natural gases.Use of compressibility factors from Fig. 23-4 should yield mix-ture volumes (densities) within 2% to 3% of the true valuesfrom a reduced temperature slightly greater than 1.0 to thelimits of the chart for both temperature and pressure. Thechart was prepared from data for binary mixtures of methanewith ethane, propane and butane and data for natural gases.No mixtures having average molecular weights greater than40 were used, and all gases contained less than 10% nitrogenand less than 2% combined hydrogen sulfide and carbon diox-ide. Fig. 23-4 is applicable for temperatures 20F or moreabove saturation and to pressures as high as 10,000 psia.

Appreciable Amount of Nonhydrocarbons Fig. 23-4 does not apply for gases or vapors with more than2% H2S and/or CO2 or more than 20% 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 weight natural gases. These figures cover awide range of molecular weights (15.95 to 26.10), tempera-tures (100 to 1000F) and pressures (up to 5,000 psia). Forgases with molecular masses between the molecular massesshown in Figs. 23-5 through 23-7, linear interpolation betweenadjacent charts should be used to compute the compressibility.

In general, compressibilities for gases with less than 5%noncondensable nonhydrocarbons, such as nitrogen, carbondioxide, and hydrogen sulfide, are predicted with less than 2%error. When molecular weight is above 20 and compressibilityis below 0.6, errors as large as 10% may occur.

Effect of Acid Gas Content Natural gases whichcontain H2S and/or CO2 exhibit different compressibility fac-tor behavior than do sweet gases. Wichert and Aziz3 present acalculational procedure to account for these differences. Themethod uses the standard gas compressibility factor chart(Fig. 23-3) 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, , 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 Eq 23-511

FIG. 23-4Compressibility Factors for Natural Gas1

23-12

FIG. 23-5Compressibility of Low-Molecular-Weight Natural Gases11

23-13

FIG. 23-6Compressibility of Low-Molecular-Weight Natural Gases11

23-14

FIG. 23-7Compressibility of Low-Molecular-Weight Natural Gases11

23-15

FIG. 23-8

Pseudocritical TemperaturPc = Pc Tc

Tc + B (1 B)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 100F and 1000 psia.

Solution Steps

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

Comp.Mole

Fraction Tc, R

Pseudo-criticalTc, R Pc, psia

Pseudo-criticalPc, psia

CO2 0.10 547.6 54.8 1071 107.1H2S 0.20 672.1 134.4 1300 260.0N2 0.05 227.2 11.4 493.1 24.7CH4 0.60 343.0 205.8 666.4 399.8C2H6 0.05 549.6 27.5 706.5 35.3

433.9 826.9

23e Adjustment Factor3, , FThe pseudocritical temperature adjustment factor is readfrom Fig. 23-8 to be 29.8F. The adjusted pseudocritical tem-perature is:

Tc = 433.9 29.8 = 404.1 R

The adjusted pseudocritical pressure is:

Pc = (826.9) (404.1)

433.9 + 0.2 (1 0.2) 29.8 = 761.7 psia

The pseudocritical temperature and pseudoreducedpressure are:

Tr = 100 + 459.67

404.1 = 1.385 Pr =

1000761.7

= 1.313

Z = 0.831 (Fig. 23-4)

(The EZ*THERMO90 version of the SRK gives Z = 0.838.)

HYDROCARBON FLUID 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.

-16

FIG. 23-9Hydrocarbon Fluid Densities2, 3, 19

23-17

FIG. 23-10Approximate Specific Gravity of Petroleum Fractions

23-18

FIG. 23-11Effect of Temperature on Hydrocarbon Liquid Densities19

23-19

FIG. 23-12Specific Gravity of Petroleum Fractions

23-20

FIG. 23-13Specific Gravity of Paraffinic Hydrocarbon Mixtures

23-21

Subcooled liquid hydrocarbon densities from 50F to+140F are shown on Fig. 23-11. Corrections to liquid hydro-carbon densities due to high pressure are shown on Fig. 23-15.

Specific gravities of petroleum fractions are given in Fig.23-12 where temperature ranges from 0 to 1000F and pres-sures from atmospheric to 1500 psia. The petroleum fractionis identified within the center grid by two of three charac-teristics API gravity at 60F, 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 thepetroleum fraction. The characterization factor, Kw, is definedin the inset example shown to illustrate use of Fig. 23-12.

The specific gravity 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 weight.

Fig. 23-13 generally predicts specific gravities within 3% ofmeasured values for paraffinic mixtures. However, the accu-racy is somewhat less for mixtures having:

Reduced temperatures above 0.9. Molecular weights 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-pane and heavier components at standard conditions, thencorrected this ideal volume using apparent densities for thegaseous components ethane and methane. The resultingpseudodensity at 60F and 14.7 psia is corrected for pressureusing a hydrocarbon liquid compressibility chart, then for tem-perature using a thermal expansion chart (Fig. 23-17) for hy-drocarbon liquids. Experience with crude oils and richabsorber oils shows this correlation will predict densitieswithin 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 60F to 240F. The following pro-cedures and charts are recommended for general applicabilityto liquids containing components heavier than pentanes (gassaturated or subcooled) at pressures up to 10,000 psia andtemperatures from 100F to 600F. Significant amounts ofnonhydrocarbons can be handled by this procedure (up to20% N2, 80% CO2, and 30% H2S).

1. Set up a calculation table as shown in the example in Fig.23-16.

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 + C2plus) fraction.

Wt % (N2 + C2) = Wt (N2 + C2)Wt (N2 + C2 plus) 100 Eq 23-823-4. 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 20F, 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 + C2 plus)

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

Eq 23-9

where

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

Density (N2 + C2 plus)6. Calculate the weight percent methane

Wt % methane = Wt methanetotal 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(60F and 14.7 psia) on the right side of the chart.

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

9. Correct the density at 60F and pressure to the actualtemperature using Fig. 23-17. Add the correction to thedensity from Step 8.

This procedure should not be used in the critical region. Mix-tures at temperatures greater than 150F which 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 data35 and errors are rarely greater than8%. The best accuracy occurs for mixtures containing mostlyC5 plus with relatively small amounts of dissolved gaseouscomponents (errors are usually less than 3%). Note that den-sities of C2 plus, C3 plus, CO2 plus, or C4 plus mixtures can becalculated by this procedure at various temperatures andpressures, and that the gaseous components need not be pre-sent.

Example 23-3 Fig. 23-16 illustrates the procedure outlinedabove.

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

= 44.836 lb1.0128 ft3

= 44.275 lb/ft3

Wt % C2 in C2 plus =

0.5670.567 + 44.836

100 = 1.25%Density of C2 plus from Fig. 23-14 = 44.0 lb/ft3

Density of CO2 plus = 45.403 + 17.485

45.40344.0

+ 0.3427 = 45.75 lb/ft322

FIG. 23-14Pseudo Liquid Density of Systems Containing Methane and Ethane

23-23

(1) (2) (3)

Component MoleFractionMolecular

WeightMethane 0.20896 16.043 Carbon Dioxide 0.39730 44.010 Ethane 0.01886 30.070 Propane 0.02387 44.097 n-Butane 0.03586 58.123 n-Pentane 0.02447 72.150 n-Hexane 0.01844 86.177 n-Heptane 0.02983 100.204 n-Octane 0.02995 114.231 n-Decane 0.18208 142.285 n-Tetradecane 0.03038 198.394 Total 1.00000

FIG. 23-15Calculation of Liquid Density of

FIG. 23-16Density Correction for Compressibility of

Hydrocarbon Liquids

23Wt % CH4 in Total = 3.35266.241

100 = 5.1%

Pseudodensity of mixture at 60F and 14.7 psia fromFig. 23-14 = 42.9 lb/cu ft

Pressure correction to 1760 psia from Fig. 23-15 = +0.7

Density at 60F and 1760 psia = 42.9 + 0.7 = 43.6 lb/ft3

Temperature correction to 120F from Fig. 23-17 = 1.8

Density at 120F and 1760 psia = 43.6 1.8 = 41.8 lb/ft3

(Density by EZ*THERMO version of SRK using Costald92

41.815 lb/ft3.

Experimental density35 at 120F and 1760 psia = 41.2 lb/ft3

Error = (41.8 41.2)/41.2 = 0.015, or 1.5%

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

Weight, lb Density (60F),lb/cu ft Volume, cu ft

3.352 17.485 51.016 0.3427

0.567 1.053 31.619 0.03332.084 36.423 0.05721.766 39.360 0.04491.589 41.400 0.03842.989 42.920 0.06963.421 44.090 0.0776

25.907 45.790 0.56586.027 47.815 0.1260

66.240

a Mixture at 120F and 1760 psiaBOILING 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 23-11Where the subscripts 10, 30, 50, 70, and 90 refer to the vol-

ume 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 23-12To use the graph, locate the curve for the distillation VABP

in the appropriate set for the type of boiling point desired. Forthe known 10-90% slope, read a correction for the VABP fromthe selected VABP curve.

-24

FIG. 23-17Density Correction for Thermal Expansion of Hydrocarbon Liquids

23-25

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

% Over Temperature, FIBP 100

5 13010 15320 19130 21740 24450 28060 31970 38480 46490 592EP 640

IBP = initial boiling point EP = end point

Slope = (592 153)/80 = 5.49

VABP = (153 + 217 + 280 + 384 + 592)/5 = 325FRefer to Fig. 23-18. Read down from a slope of 5.49 to the

interpolated curve for 325F in the set drawn with dashedlines (MeABP). Read a correlation value of 54 on the ordinate.Then:

MeABP = 325 54 = 271F

The significance of the various average boiling points, inter-conversion of D-86 and D-1160 ASTM distillations, and thecalculation of true-boiling point and atmospheric flash curvesfrom ASTM distillation data can be found in Chapters 3 and4 of the API Technical Data Book.36

Molecular weight can be calculated from Eq 23-13 using Me-ABP in R and S (specific gravity at 60F) .

MW = 204.38 [(T)0.118] (S1.88) (e(0.00218 T 3.075 S)) Eq 23-13This relationship has been evaluated in the molecular

weight range of 70 to 720; the MeABP range of 97 to 1040F;and the API range of 14 to 93. The average error was about7%. Eq. 23-13 is best used for molecular weights above 115,since it tends to over-predict below this value.Example 23-5 Calculation of molecular weight.From Example 23-4:

S = 0.7515 for 56.8 API

MeABP = 271 + 460 = 731R

Using Eq 23-13,

MW = 204.38[(731)0.118][(0.7515)1.88][e(0.00218 731) (3.075 0.7515)] = 127.0

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-

FIG. 23-18

Characterizing Boiling Points of Petroleum23 Fractions (From API Technical Data Book)-26

FIG. 23-19Low-Temperature Vapor Pressures for Light Hydrocarbons

23-27

FIG. 23-20High-Temperature Vapor Pressures for Light Hydrocarbons

23-28

FIG. 23-21Viscosities of Hydrocarbon Liquids

23-29

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 = [3.12281 (109) T 2.3125] S 2.3201 Eq 23-14Tpc = 24.2787 T

0.58848 S0.3596 Eq 23-15These equations are in terms of T = MeABP (R) and specific

gravity (S) at 60F. Both of these correlations have been evalu-ated over the range of 80 to 690 molecular weight; 70 to 295Fnormal 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 = 325FMeABP = 271FAPI = 56.8Molecular Weight = 127 (Ex. 23-5)ASTM D-86, 10% to 90% Slope = 5.49

Find its pseudocritical temperature.Solution Steps

From Fig. 23-18 with ASTM D-86 slope = 5.49 find a VABPcorrection of about 85F (extrapolated from the left-handgroup).

MABP = 325 85 = 240F

Use Eq 23-15 to calculate the pseudocritical temperature as:

Tpc = 24.2787 (271 + 460)0.58848 (0.7515)0.3596

= 1062R or 602F

For this 56.8 API fluid, estimate the pseudocritical pres-sure, using Eq 23-14 and MeABP = 271F:

Ppc = [3.12281 (109)] (271 + 460)2.3125 (0.7515)2.3021= 386 psia

Acentric FactorThe acentric factor, , 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

= log (Pvp/Pc) Tr = 0.7 1.0 Eq 23-16This definition requires knowledge of the critical (pseudo-

critical) temperature, vapor pressure, and critical (pseudo-critical) pressure.

For a hydrocarbon mixture of known composition, and con-taining similar components, the acentric factor may be esti-mated, with reasonable accuracy, as the molar average of theindividual pure component acentric factors:

= xi i Eq 23-17

FIG. 23-22Viscosity of Paraffin Hydrocarbon Gases at One Atmosphere23-30

FIG. 23-23Hydrocarbon Gas Viscosity

23-31

If the vapor pressure is not known, can be estimated38 forpure hydrocarbons or fractions with boiling point ranges of50F or less, using Eq. 23-18.

= 37

log Pc log 14.7

TcTb

1 1.0 Eq 23-18

Example 23-7 Acentric factor.A narrow-boiling petroleum fraction has a VABP of 418F,

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 ofMABP); and the pseudocritical pressure (a function of Me-ABP).

From Fig. 23-18, the correction to VABP for mean averageis 3F; the correction for MABP is 5F. Note that for narrow-boiling fractions, all boiling points approach the volumetricaverage. Then, MeABP = 415F and MABP is 413F.

From Eq. 23-14, the pseudocritical pressure is:

T = 415 + 460 = 875R

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

Ppc = [3.12281 109 (875)2.3125] (0.871)2.3201

Ppc = 356 psiaFrom Eq. 23-15, the pseudocritical temperature is:

Tpc = 24.2787 (875)0.58848 (0.871)0.3596

Tpc = 1244R

= 37

log (356) log (14.7)

1244875

1.0 1.0 = 0.447

Vapor PressureThe vapor pressures of light hydrocarbons and some com-

mon inorganics in the temperature range below 100F aregiven in Fig. 23-19. Vapor pressures at higher temperatures,up to 600F, are given in Fig. 23-20 for the same compounds.Note that, except for ethylene and propylene, the hydrocar-bons 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 and23-24 present data on hydrocarbon gases. To correct for pressure,the gas viscosity from Fig. 23-22 is adjusted from atmospheric

FIG. 23-24Viscosity Ratio vs. Pseudoreduced Temperature23-32

FIG. 23-25Viscosity of Miscellaneous Gases One Atmospherepressure values by Figs. 23-23 and 23-24. Fig. 23-24 is pre-ferred when the reduced temperature is greater than 1.0. Fig.23-28 gives the viscosity of hydrocarbon liquids containing dis-solved gases. Note that Fig. 1-7 gives conversion factors forviscosity.

Calculation of Gas Mixture ViscosityExample 23-8Determine the viscosity of a gas of molecularweight 22 at 1,000 psia and 100F. Tc = 409R, Pc = 665 psia

Solution Steps

Gid = 22/28.964 = 0.760

From Fig. 23-23 at 100F:

A = 0.0105 centipoiseThen:

Tr = 100 + 460

409 = 1.37 Pr =

1000665

= 1.50

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 to obtain the cor-rection for elevated pressure to the viscosity at one atmos-phere.From Fig. 23-24:

A

= 1.21

23-3FIG. 23-26Viscosity of Air43, 44, 45Hence, the viscosity at 1000 psia and 100F is:

= (1.21) (0.0105) = 0.0127 centipoiseThe viscosity of a gaseous mixture with large amounts of

nonhydrocarbons 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 3525 psia. It makes use of a factor, ,defined as:

= 5.4402

(Tcm)1/6

( (xi MWi) (Pcm ))2/3

Eq 23-19

If the reduced temperature Tr is > 1.5, then

A = [166.8 (105)] [(166.8 105)(0.1338 Tr 0.0932)5/9]Eq 23-20

If Tr is 1.5,

A = 34.0 105 (Tr 8/9 ) Eq 23-21In either case, A is found by dividing ( A) by .

Equations 23-19 through 23-21 will predict the viscosity of puregases as well as mixtures. To apply the Dean and Stiel41 methodto mixtures, the pseudocritical volumes, compressibilities, andtemperatures are calculated by the Prausnitz and Gunn42 mixingrules:

3

Vcm = (yi Vci) Eq 23-22 B = 1105.7

A = 101.78 (325 + 459.67) 0.175 29.263

11.991105.3

= 0.02645

The same constants are employed at 100F and at 210F.

= 0.02645 e1.8 (1105.7)

559.67 = 0.926 cs at 100F

= 0.02645 e1.8 (1105.7)

669.67 = 0.517 cs at 210F

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 23-36 present lowpressure thermal conductivity data of gases developed frompublished data.51, 54 The pressure correction of Lenoir et al.52shown 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.

FIG. 23-27Water Viscosity at Saturated ConditionsZcm = (yi Zci) Eq 23-23Tcm = (yi Tci) Eq 23-24

Pcm = Zcm R Tcm

VcmEq 23-25

Example 23-9 For a temperature of 50F and a pressure of300 psia, estimate the viscosity of a mixture of 80 mole percentmethane, 15 mole percent nitrogen, and 5 mole percent carbondioxide. Calculations are summarized in Fig. 23-30:

Pcm = Zcm R Tcm

Vcm

= (0.2875) (10.73) (335.9)

1.562 = 663.4 psia

Substituting from the calculation table in Fig. 23-30 intoEq 23-19:

= (5.4402) (335.9)1/6

(19.237)1/2 (663.4)2/3 = 0.043

Tr = T

Tcm = 509.7

335.9 = 1.517

Because Tr > 1.5, the expression to be used for A is Eq 23-20.

A = 166.8 (105) [0.1338 Tr 0.0932]5/9= 166.8 (105) [(0.1338) (1.517) 0.0932]5/9

A = 48.91 (105)A = 0.01138 centipoise

Using Fig. 23-23 and correcting for the nitrogen and carbondioxide content of this mixture gives a A of 0.0116 cp. This is agood check. Had a 20% N2 content been chosen for this example,the N2 range of Fig. 23-23 would have been exceeded and use ofthe Dean and Stiel method would have been required. When theconditions at hand fall within the limits of Fig. 23-23, use thisfigure and not the Dean and Stiel correlation.

Viscosity of Petroleum FractionsMid-Boiling Point Method The viscosity of a crude

oil 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.

= A e1.8 B / T Eq 23-26

A = (101.78 Tb 0.175 29.263) KwB

Eq 23-27

ln (B) = 4.717 + 0.00292 Tb Eq 23-28Example 23-10 At 100F and 210F find the viscosity of aheavy condensate having a mid-boiling point of 325F and aspecific gravity of 0.7688.

Solution Steps

Kw = 3 325 + 459.67

0.7688 = 11.99

ln (B) = 4.717 + (0.00292) (325 + 459.67) = 7.0123-34

FIG. 23-28Liquid Viscosity of Pure and Mixed Hydrocarbons Containing Dissolved Gases at 100F and One Atmosphere

23-35

k/kA = 1.15

k = (1.15) (0.0248) = 0.0285 Btu/[(hr sq ft F)/ft]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 charts pro-vided and the thermal conductivity of the mixture isdetermined by the cube root rule.56 This rule is applicableto mixtures of simple gases; it does not apply to mixtures con-taining CO because the thermal conductivity goes through a

FIG. 23-29Viscosity of Steam46, 47Example 23-11 Find the thermal conductivity of a 25 mo-lecular weight natural gas at 700 psia and 300F. Tc = 440R,Pc = 660 psia

Solution Steps

From Fig. 23-31, at 300F:

kA = 0.0248 Btu/[(hr sq ft F)/ft]Tr = (300 + 460)/440 = 1.73Pr = 700/660 = 1.06

From Fig. 23-32:

Mole Fraction

MolecularWeight Tc, R Pc, psia

CH4 0.80 16.043 343.0 666.4 N2 0.15 28.013 227.2 493.1 CO2 0.05 44.010 547.6 1071. Mixture 1.00

FIG. 2Calculation of Viscos

23-2maximum.

km = (yi ki 3MWi )

yi 3MWi

Eq 23-29

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 thegaseous mixture shown in Fig. 23-37 at 200F and one at-mosphere.

km = 0.057742.822

= 0.0205 Btu/[(hr sq ft F)/ft]

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. Vargaftik62and Touloukian65 each have extensive collections of experi-mental data.

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.

VC,cu ft/lb mole Zc =

PcVc10.73 Tc

Vcm = yiVci Tcm = yiTci MWm = yiMWi

1.59 0.2879 1.272 274.4 12.8341.43 0.2892 0.215 34.1 4.2021.51 0.2752 0.076 27.4 2.2011.562 0.2875 1.562 335.9 19.237

3-30ity of a Gas Mixture36

FIG. 23-31Thermal Conductivity of Natural and Hydrocarbon Gases

at One Atmosphere (14.696 psia)Pure ComponentsThe surface tension of pure hydrocarbons as a function of

temperature may be obtained from Fig. 23-38.

MixturesSurface tension for binaries of known composition at or near

atmospheric pressure may be calculated78 using:

m = 1 2

1 x2 + 2 x1Eq 23-30

The presence of inert gases, such as N2 and CO2, in the liquidphase tends to lower the surface tension of the liquid. Wherethe concentration of inert gases in the liquid exceeds 1.0 mole%, estimated values of surface tension may be 5 to 20% higherthan actual values for the mixture.

GROSS HEATING VALUE OF NATURALGASES

The gross heating value, specific gravity, 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 = (yiHvi) Eq 23-31

23-FIG. 23-32Thermal Conductivity Ratio for GasesValues 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.

Specific gravity (also termed relative density 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).

G = s

= MW P Ta ZaMWa Pa Z

Eq 23-32

The ideal gas specific gravity is the ratio of the molecularweight of the gas to the molecular weight of dry air.

Gid = MWMWa

Eq 23-33

For a mixture

G id = (yi Gi id) Eq 23-34The specific gravity G is measured and is generally used to

calculate the molecular weight ratio Gid when the gas compo-sition is not available.

37

FIG. 23-33Thermal Conductivity of Miscellaneous Gases

at One Atmosphere59, 60, 61, 62G id = MWMWa

= G (Pa T Z)

P Ta ZEq 23-35

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 = Pwo

p =

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

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

yiw = yi 1

Pw

o

P = yi (1 yw) Eq 23-36

For water saturated gas, water is added to the componentlist and the xiw 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 (satd) = 1

1.7051P

Hv (dry) +

1.7051 29.94P

Eq 23-37

23-FIG. 23-34Thermal Conductivity of Hydrocarbon Gases

at One Atmosphere67, 68, 69When 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 fromEq 23-37.

The yi w values are used in the gross heating value and gascompressibility 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 23-38Calculations Additional details on these calculational

methods and examples are given in GPA Standard 2172, Cal-culation of Gross Heating Value, Relative Density and Com-pressibility Factor for Natural Gas Mixtures fromCompositional Analysis. A listing of the Basic source code fora computer program to perform the calculations is given in2172.

REFERENCES

1. Standing, M. B. and Katz, D. L., Trans. AIME 146, 159 (1942).

2. Pitzer, K. S., et al., J. Am. Chem. Soc. 77, 3433 (1955).

3. Wichert, E. and Aziz, K., Hyd. Proc. 51, 199 (May, 1972).

4. Hall, K. R. and Yarborough, L., Oil Gas J. 71, No. 25, 82 (June 18,1973).

5. Hall, K. R. and Yarborough, L., Oil Gas J. 72, No. 7, 86 (Feb. 18,1974).

38

FIG. 23-35Thermal Conductivity of Liquid Paraffin Hydrocarbons

FIG. 23-36Thermal Conductivity of Liquid Petroleum Fractions58

23-39

Component MoleFraction

ThermalConductivity

Btu/[(hr sq ft F)/ft]Molecular

Weight3MWi (yi 3MWi) (yi ki 3MWi )

CO2 0.10 0.0127 44.010 3.530 0.3530 0.00448

H2S 0.20 0.0136 34.076 3.242 0.6484 0.00882

N2 0.05 0.0175 28.013 3.037 0.1519 0.00266

CH4 0.60 0.0258 16.043 2.522 1.5132 0.03904

C2H6 0.05 0.0176 30.070 3.109 0.1555 0.00274

Total 1.00 2.8220 0.05774

FIG. 23-37Calculation of Thermal Conductivity

FIG. 23-38Surface Tension of Paraffin Hydrocarbons85

23-40

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Table of ContentsViewing RecommendationsSearch the Data BookHelpData Book HelpReader Online GuideSearch Online Guide

Section 23 Physical PropertiesCOMPUTER PREDICTION METHODSCOMPRESSIBILITY OF GASESPure GasesGas MixturesMinor Amounts of NonhydrocarbonsAppreciable Amount of NonhydrocarbonsEffect of Acid Gas Content

HYDROCARBON FLUID DENSITIESData and CorrelationsDensity of Saturated and Subcooled Liquid Mixtures

BOILING POINTS, CRITICAL PROPERTIES, ACENTRIC FACTOR, VAPOR PRESSUREBoiling PointsCritical PropertiesAcentric FactorVapor Pressure

VISCOSITYCalculation of Gas Mixture ViscosityViscosity of Petroleum FractionsMid-Boiling Point Method

THERMAL CONDUCTIVITYTRANSPORT PROPERTY REFERENCESSURFACE TENSIONPure ComponentsMixtures

GROSS HEATING VALUE OF NATURAL GASESGross Heating ValueSpecific gravityCorrections for Water ContentCalculations

REFERENCESFIGURESFIG. 23-1: NomenclatureFIG. 23-2: Physical ConstantsAcentric factorAir required for combustion, ideal gasASTM octane number Motor method, Research methodBoiling point, FCompressiblity factor of real gasDenisty of liquid Relative density, lb/gal, gal/lbmolFlammability limits, vol% in airFreezing pointHeat of vaporizationHeating value, 60 F Net, GrossIdeal gas Relative density, cu ft gas/lb, cu ft gas/gal liquidMolar massPressureRefractive indexSpecific heat Ideal gas, LiquidTemperature, FTempurature coefficient of densityVapor pressureVolume

FIG. 23-2 (Contd): Notes and References for the Table of Physical ConstantsFIG. 23-2 (Contd): Notes for the Table of Physical ConstantsFIG. 23-3: Calculation of Pseudocritical Temperature and Pressure for a Natural Gas MixtureFIG. 23-4: Compressibility Factors for Natural GasFIG. 23-5: Compressibility of Low-Molecular-Weight Natural GasesFIG. 23-6: Compressibility of Low-Molecular-Weight Natural GasesFIG. 23-7: Compressibility of Low-Molecular-Weight Natural GasesFIG. 23-8: Pseudocritical Temperature Adjustment Factor , FFIG. 23-9: Hydrocarbon Fluid DensitiesFIG. 23-10: Approximate Specific Gravity of Petroleum FractionsFIG. 23-11: Effect of Temperature on Hydrocarbon Liquid DensitiesFIG. 23-12: Specific Gravity of Petroleum FractionsFIG. 23-13: Specific Gravity of Paraffinic Hydrocarbon MixturesFIG. 23-14: Pseudo Liquid Density of Systems Containing Methane and EthaneFIG. 23-15: Calculation of Liquid Density of a Mixture at 120F and 1760 psiaFIG. 23-16: Density Correction for Compressibility of Hydrocarbon LiquidsFIG. 23-17: Density Correction for Thermal Expansion of Hydrocarbon LiquidsFIG. 23-18: Characterizing Boiling Points of Petroleum Fractions (From API Technical Data Book)FIG. 23-19: Low-Temperature Vapor Pressures for Light HydrocarbonsFIG. 23-20: High-Temperature Vapor Pressures for Light HydrocarbonsFIG. 23-21: Viscosities of Hydrocarbon LiquidsFIG. 23-22: Viscosity of Paraffin Hydrocarbon Gases at One AtmosphereFIG. 23-23: Hydrocarbon Gas ViscosityFIG. 23-24: Viscosity Ratio vs. Pseudoreduced TemperatureFIG. 23-25: Viscosity of Miscellaneous Gases One AtmosphereFIG. 23-26: Viscosity of AirFIG. 23-27: Water Viscosity at Saturated ConditionsFIG. 23-28: Liquid Viscosity of Pure and Mixed Hydrocarbons Containing Dissolved Gases at 100F and One AtmosphereFIG. 23-29: Viscosity of SteamFIG. 23-30: Calculation of Viscosity of a Gas MixtureFIG. 23-31: Thermal Conductivity of Natural and Hydrocarbon Gases at One Atmosphere (14.696 psia)FIG. 23-32: Thermal Conductivity Ratio for GasesFIG. 23-33: Thermal Conductivity of Miscellaneous Gases at One Atmosphere at One AtmosphereFIG. 23-34: Thermal Conductivity of Hydrocarbon Gases at One Atmosphere at One AtmosphereFIG. 23-35: Thermal Conductivity of Liquid Paraffin HydrocarbonsFIG. 23-36: Thermal Conductivity of Liquid Petroleum FractionsFIG. 23-37: Calculation of Thermal ConductivityFIG. 23-38: Surface Tension of Paraffin Hydrocarbons