SECTION 23

Physical Properties

M

This section contains a number of charts, correlations, andprocedures 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-

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 °ReABP = Mean average boiling point, °F or °R

n = number of moles, (mass/Mole weight)P = pressure, psia

Pc′ = pseudocritical pressure adjusted for acid gascomposition, psia

Pvp = vapor pressure at a reduced temperature of 0.7Pw

o = vapor pressure of water, 0.25636 psia at 60°FR = 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°/60°FT = 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

FIG.

Nomen

23

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, 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

Greekε = pseudocritical temperature adjustment factor,

Eq 23-6θ = MeABP/Tpc

ρ = density, lb/cu ftµ = viscosity at operating temperature and pressure,

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

temperature, centipoiseξ = 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

-1

FIG. 23-2

Physical Constants

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

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 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 60°F 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 0°C = 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 (Cont’d)

Notes for the Table of Physical Constants

23-8

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.

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 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.

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.

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

FIG.

Calculation of Pseudocr itical Temperatur

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 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 23-1

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-temperature-volume relationships may be made with as muchease at high pressure as at low pressure.

The equation used to calculate gas density is:

ρ = MW • P

10.73 • T • ZEq 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

23-3

e and Pr essure f or a Natur al 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 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 = Σ(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 50°F 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 properties

Using Fig. 24-26, the P-H diagram for propane, calculate thedensity of propane vapor at 200°F and 100 psia.

Solution Steps

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

ρ = 1/1.5 = 0.667 lb.ft3

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

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

Z = MW • PR • T • ρ

= (44.10) (100)

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

The SRK calculation gives ρ = 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. 23-41

shows 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 20°F 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 1000°F) 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,” 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 Ad justment Factor3, ε, °F

Pc′ = Pc Tc′

Tc + B′ (1 − B′)εEq 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 100°F 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

23

The pseudocritical temperature adjustment factor is readfrom Fig. 23-8 to be 29.8°F. 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. 23-9

Hydrocarbon Fluid Densities 2, 3, 19

23-17

FIG. 23-10

Approximate Specific Gravity of Petroleum Fractions

23-18

FIG. 23-11

Effect of Temperature on Hydrocarbon Liquid Densities 19

23-19

FIG. 23-12

Specific Gravity of Petroleum Fractions

23-20

FIG. 23-13

Specific Gravity of Paraffinic Hydrocarbon Mixtures

23-21

Subcooled liquid hydrocarbon densities from –50°F to+140°F 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 1000°F 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 60°F, 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.

Densi ty o f 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 60°F 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 60°F to 240°F. 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 –100°F to 600°F. 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 23-8

23-

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 –20°F, 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 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(60°F 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 60°F 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 150°F 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/ft3

22

FIG. 23-14

Pseudo Liquid Density of Systems Containing Methane and Ethane

23-23

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

Component MoleFraction

MolecularWeight Weight, lb Density (60°F),

lb/cu ft Volume, cu ft

Methane 0.20896 16.043 3.352 – –Carbon Dioxide 0.39730 44.010 17.485 51.016 0.3427Ethane 0.01886 30.070 0.567 – –Propane 0.02387 44.097 1.053 31.619 0.0333n-Butane 0.03586 58.123 2.084 36.423 0.0572n-Pentane 0.02447 72.150 1.766 39.360 0.0449n-Hexane 0.01844 86.177 1.589 41.400 0.0384n-Heptane 0.02983 100.204 2.989 42.920 0.0696n-Octane 0.02995 114.231 3.421 44.090 0.0776n-Decane 0.18208 142.285 25.907 45.790 0.5658n-Tetradecane 0.03038 198.394 6.027 47.815 0.1260Total 1.00000 66.240

FIG. 23-15

Calculation of Liquid Density of a Mixtur e at 120°F and 1760 psia

FIG. 23-16

Density Correction for Compressibility of Hydr ocarb on L iquids

23

Wt % CH4 in Total = 3.35266.241

• 100 = 5.1%

Pseudodensity of mixture at 60°F 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 60°F and 1760 psia = 42.9 + 0.7 = 43.6 lb/ft3

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

Density at 120°F 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 120°F and 1760 psia = 41.2 lb/ft3

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

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 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 23-12

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, read a correction for the VABP fromthe selected VABP curve.

-24

FIG. 23-17

Density 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 = 325°F

Refer to Fig. 23-18. Read down from a slope of 5.49 to theinterpolated curve for 325°F in the set drawn with dashedlines (MeABP). Read a correlation value of –54 on the ordinate.Then:

MeABP = 325 − 54 = 271°F

FIG.

Character izing B oiling Points of Petro leum

23

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 60°F) .

MW = 204.38 [(T)0.118] (S1.88) (e(0.00218 T − 3.075 S)) Eq 23-13

This relationship has been evaluated in the molecularweight range of 70 to 720; the MeABP range of 97 to 1040°F;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 = 731°R

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-

23-18

Fract ions (From API Technical Data Book)

-26

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

23-27

FIG. 23-20

High-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 23-14

Tpc = 24.2787 • T0.58848 • S0.3596 Eq 23-15

These equations are in terms of T = MeABP (°R) and specificgravity (S) at 60°F. Both of these correlations have been evalu-ated over the range of 80 to 690 molecular weight; 70 to 295°Fnormal 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 = 325°FMeABP = 271°FAPI = 56.8°Molecular 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 –85°F (extrapolated from the left-handgroup).

MABP = 325 − 85 = 240°F

FIG. 2

Viscosity of Paraff in Hydr ocarb

23-

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

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

= 1062°R or 602°F

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

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

= 386 psia

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 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:

ω = Σ xi ωi Eq 23-17

3-22

on Gases at One Atm osphere

30

FIG. 23-23

Hydrocarbon Gas Viscosity

23-31

If the vapor pressure is not known, ω can be estimated38 forpure hydrocarbons or fractions with boiling point ranges of50°F 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 418°F,

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 –3°F; the correction for MABP is –5°F. Note that for narrow-boiling fractions, all boiling points approach the volumetricaverage. Then, MeABP = 415°F and MABP is 413°F.

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

T = 415 + 460 = 875°R

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

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

FIG. 2

Viscosity Ratio vs . Pseu

23-

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

Tpc = 24.2787 • (875)0.58848 • (0.871)0.3596

Tpc = 1244°R

ω =

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 100°F aregiven in Fig. 23-19. Vapor pressures at higher temperatures,up to 600°F, 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

3-24

doreduc ed Temperature

32

FIG. 23-25

Viscos ity of Miscellaneous Gases – One Atmosp hereFIG. 23-26

Viscosity of A ir43, 44, 45

pressure 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 23-8—Determine the viscosity of a gas of molecularweight 22 at 1,000 psia and 100°F. Tc = 409°R, Pc = 665 psia

Solution Steps

Gid = 22/28.964 = 0.760

From Fig. 23-23 at 100°F:

µA = 0.0105 centipoise

Then:

Tr = 100 + 460

409 = 1.37 Pr = 1000

665 = 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:

µµA

= 1.21

23-3

Hence, the viscosity at 1000 psia and 100°F is:

µ = (1.21) (0.0105) = 0.0127 centipoise

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

ξ = 5.4402

(Tcm)1/6

(Σ (xi MWi) (Pcm ))2/3

Eq 23-19

If the reduced temperature Tr is > 1.5, then

ξ µA = [166.8 (10−5)] [(166.8 • 10−5)(0.1338 Tr − 0.0932)5/9]Eq 23-20

If Tr is ≤ 1.5,

ξ µA = 34.0 10−5 (Tr 8/9 ) Eq 23-21

In either case, µA is found by dividing (ξ µA) by ξ.Equations 23-19 through 23-21 will predict the viscosity of pure

gases 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

FIG. 23-27

Water Viscosity at Saturated Conditions

Vcm = Σ (yi Vci) Eq 23-22

Zcm = Σ (yi Zci) Eq 23-23

Tcm = Σ (yi Tci) Eq 23-24

Pcm = Zcm R Tcm

VcmEq 23-25

Example 23-9 — For a temperature of 50°F 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:

ξ = (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 ξµA is Eq 23-20.

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

= 166.8 (10−5) [(0.1338) (1.517) − 0.0932]5/9

ξ µA = 48.91 (10−5)

µA = 0.01138 centipoise

Using Fig. 23-23 and correcting for the nitrogen and carbondioxide content of this mixture gives a µA 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.

η = A • e1.8 B / T Eq 23-26

A = (101.78 Tb − 0.175 − 29.263)

Kw

BEq 23-27

ln (B) = 4.717 + 0.00292 Tb Eq 23-28

Example 23-10 — At 100°F and 210°F find the viscosity of aheavy condensate having a mid-boiling point of 325°F 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) = 7.01

23-3

B = 1105.7

A = 101.78 (325 + 459.67) − 0.175 − 29.263

11.991105.3

= 0.02645

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

η = 0.02645 • e1.8 (1105.7)

559.67 = 0.926 cs at 100°F

η = 0.02645 • e1.8 (1105.7)

669.67 = 0.517 cs at 210°F

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.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.

4

FIG. 23-28

Liquid Viscosity of Pure and Mixed Hydrocarbons Containing Dissolved Gases at 100°F and One Atmosphere

23-35

FIG. 23-29

Viscosity of Steam46, 47

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

Solution Steps

From Fig. 23-31, at 300°F:

kA = 0.0248 Btu/[(hr • sq ft • °F)/ft]

Tr = (300 + 460)/440 = 1.73

Pr = 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. 2

Calculation of Viscos

23-

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 CO2 because the thermal conductivity goes through amaximum.

km = Σ (yi ki

3√MWi )

Σ yi 3√MWi

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 200°F 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. Vargaftik62

and 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 =

PcVc

10.73 TcVcm = ΣyiVci Tcm = ΣyiTci MWm = ΣyiMWi

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

3-30

ity of a Gas Mixture

36

FIG. 23-31

Thermal Con ductivity of Natural and Hy drocarbon Gas esat One Atmosphere (14.696 psia)

FIG. 23-32

Thermal Conduc tivity Ratio for Gases

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:

σm = σ1 • σ2

σ1 • x2 + σ2 • 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 = Σ (yiHvi) Eq 23-31

23-

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.

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 = ρρs

= MW P Ta Za

MWa Pa ZEq 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 = Σ (yi Gi id) Eq 23-34

The specific gravity G is measured and is generally used tocalculate the molecular weight ratio Gid when the gas compo-sition is not available.

37

FIG. 23-33

Thermal Conductivity of Miscellaneous Gases at One Atmosphere 59, 60, 61, 62

FIG. 23-34

Thermal Conductivity of Hydrocarbon Gases at One Atmosphere 67, 68, 69

G 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 = Pw

o

p =

nw

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

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

yiw = yi

1 −

Pwo

P

= yi (1 − yw) Eq 23-36

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 • 29.94

P

Eq 23-37

23-

When 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 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 23-38

Calculations — Additional details on these calculationalmethods 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. 23-35

Thermal Conductivity of Liquid Paraffin Hydrocarbons

FIG. 23-36

Thermal Conductivity of Liquid Petroleum Fractions 58

23-39

Component MoleFraction

ThermalConductivity

Btu/[(hr • sq ft • °F)/ft]

MolecularWeight

3√MWi (yi

3√MWi) (yi ki

3√MWi )

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. 23-37

Calculation of Thermal Conductivity

FIG. 23-38

Surface Tension of Paraffin Hydrocarbons 85

23-40

6. Robinson, R. L., Jr. and Jacoby, R. H., Hyd. Proc. 44, 141 (April,1965).

7. Benedict, M., Webb, G. B., and Rubin, L. C., Chem. Eng. Prog.47, No. 8, 419 (1951).

8. Starling, K. E. and Han, M. S., Hyd. Proc. 50, 129 (March, 1971).

9. Hopke, S. W. and Lin, C. J., 76th Nat’l AIChE Meeting, Tulsa,Oklahoma, March, 1974.

10. George, B. A., Proc. 61st Ann. Conv. GPA, Dallas, Texas, p. 171(March 15-17, 1982).

11. Brown, G. G., Katz, D. L., Oberfell, G. G., and Alden, R. C., “Natu-ral Gasoline and the Volatile Hydrocarbons,” Natural Gas Assoc.of America, Tulsa, Oklahoma, 1948.

12. API Research Project 44, “Selected Values of Properties of Hydro-carbons and Related Compounds,” Thermodynamic ResearchCenter, Texas A&M University.

13. Starling, K. E., “Fluid Thermodynamic Properties for Light Pe-troleum Systems,” Gulf Publ. Co., Houston, 1973.

14. Physical Property Data Service, Institution of Chemical Engi-neers, 165-171 Railway Terrace, Rugby, Warwickshire, U.K.

15. TRAPP by J. F. Ely and H. J. M. Hanley, U.S. National Bureauof Standards, National Engineering Laboratory, ThermophysicalProperties Division, Boulder, Colorado 80303 (1983).

16. Petercon, J. N., Chem, C. C., and Evans, L. B., Chem. Eng. 85,79 (July 31, 1978).

17. Garrett, J. R., Chem. Eng. 90, 149 (March 7, 1983).

18. “AIChE Applications Software Survey for Personal Computers1984,” American Institute of Chemical Engineers, New York, NY,1984.

19. Deam, J. R., Kellizy, I. K. and Maddox, R. N., “Calculating Den-sity of Saturated Hydrocarbon Mixtures,” Proc. 48th Ann. Conv.NGPA, Dallas, Texas, pp. 48-51 (March 1969).

20. Kay, W. B., J. Chem. Eng. Data, 15, 46 (1970).

21. Kay, W. B., Ind. Eng. Chem., 32, 353 (1940).

22. Gugnoni, R. J., Eldridge, J. W., Okay, V. C. and Lee, T. J., AIChEJ. 20, 367 (1974).

23. Reamer, H. H., Sage, B. H., and Lacey, W. N., Ind. Eng. Chem.,43, 2515 (1951).

24. Sage, B. H. and Lacey, W. N., API Research Project 37 (1955).

25. Kay, W. B. and Price, D. B., Ind. Eng. Chem., 45, 615 (1953).

26. Kay, W. B. and Rambosek, G. M., Ind. Eng. Chem., 45, 221 (1953).

27. Bierlein, J. A. and Kay, W. B., Ind. Eng. Chem., 45, 618 (1953).

28. Arai, Y., Kaminishi, G. and Saito, S., J. Chem. Eng. of Japan, 4,No. 2, 113 (1971).

29. Chappelear, P. S., “Low Temperature Data from Rice Universityfor Vapor-Liquid and P-V-T Behavior,” GPSA TP-4 (April 1974).

30. Hiza, M. J. and Haynes, W. M., J. Chem. Thermodynamics, 9,873 (1977).

31. Hiza, M. J. and Haynes, W. M., J. Chem. Thermodynamics, 12,1 (1980).

32. Haynes, W. M. and Hiza, M. J., J. Chem. Thermodynamics, 12,179 (1980).

33. Huang, E. T. S., Swift, G. W. and Kurata, F., AIChE J., 13, 846(1967).

34. Gonzalez, M. H. and Lee, A. L., J. Chem. Eng. Data, 13, 172(1968).

35. Turek, E. A., Metcalfe, R. S., Yarborough, L., and Robinson, R. L.,DPE 9231 Presented at 55th Annual Fall Meeting of Soc. Pet.Engrs., Dallas, Sept. 21-24, 1980.

23-

36. Technical Data Book – Petroleum Refining American PetroleumInst., Washington, D.C. Procedures a: 4D4.1 (1980; b: 4D3.1(1980); c: 4D3.2 (1980); d: 2B2.1.

37. Lee, B. I. and Kesler, M., AIChE J. 21, 510 (1975).

38. Edmister, W. C., Pet. Refiner, 37 (4), 173 (1958).

39. Smith and Watson, Courtesy of Brown and Root Inc.

40. Edmister, W. C., “Applied Thermodynamics,” The Gulf Publish-ing Co., Houston, 1961.

41. Dean, D. E. and Stiel, L. I., AIChE J., 11, 526 (1965).

42. Prausnitz, J. M. and Gunn, R. D., AIChE J., 4, 430 (1958).

43. Granet, I., and Kass, P., Pet. Ref. 31 (10), 113 (1952).

44. Kester, J., and Leidenfrost, W., “Thermodynamic and TransportProperties of Gases, Liquids and Solids,” p. 321, McGraw HillBook Co., Inc., New York, NY, 1959.

45. Thermodynamic Properties Research Center Data Book 2 Table2048 (December 1962), Purdue University, Lafayette, Indiana.

46. Saline Water Conversion Engineering Data Book, 2nd Ed., U.S.Dept. of the Interior, Washington, D.C., November 1971.

47. Kestin, J., and Wang, H. E., Physica 26, 575 (1960).

48. A.S.T.M. Standard Viscosity-Temperature Chart 0361-39 Nat.Bur. Stds. Circular C461 (1947).

49. Amin, M. B., and Maddox, R. N., Hyd. Proc. 59, 131 (December1980).

50. Riazi, M., Prediction of Thermophysical Properties of PetroleumFractions, PhD Thesis, Pennsylvania State University, pp. 44 etseq., August 1979.

51. “Self Consistent Correlation of Thermodynamic and TransportProperties,” K. E. Starling, et al., GRI/AGA Project No. Br-111-1;OU-ORA Project No. 2036 156-716. Report: GR/AGA/BR-111-1/77-36.

52. Lenoir, J. M., Junk, W. A., and Comings, E. W., Chem. Eng. Progr.,49, 539 (1953).

53. Smith, W. J. S., Durbin, L. D., and Kobayashi, R., J. Chem. Eng.Data, 5, 316 (1960).

54. Katz, D. L., Cornell, D., Kobayashi, R., Poetmann, F. H., Vary, J.A., Elenbaas, J. R., and Weinaug, C. F., “Handbook of NaturalGas Engineering,” McGraw-Hill, New York, 1959.

55. Li, C. C., AIChE J., 22, 927 (1976).

56. Friend, L., and Adler, S. B., “Transport Properties of Gases,”pp. 128-131, Cambel and Fenn, Ed., Northwestern Univ. Press,Evanston, Illinois, 1958.

57. Engineering Science Data Unit. No. 75003, June, 1975.

58. Mallan, G. et al., J. Chem, Eng. Data 12, 412 (1972).

59. Hanley, H. J. M. and Ely, J. F., J. Phys. Chem. Ref. Data, 2, 735(1973).

60. Harrath, A. L., “Physical Properties of Inorganic Compounds –SI Units,” Crane, Russak and Co., Inc., New York, 1975.

61. Vasserman, A. A., Kazarchinski, Ya Z. and Rabinovich, V. A.,“Thermophysical Properties of Air and Air Compounds,” pp. 356-70, U.S. Dept. of Commerce, Springfield, VA, 1971.

62. Vargaftik, N. B., “Tables on the Thermophysical Properties ofLiquids and Gases,” 2nd Ed., p. 208, p. 346, John Wiley & Sons,New York, NY, 1975.

63. Carmichael, L. T., and Sage, B. H., J. Chem. Eng. Data, 9, 501(1964).

64. Kramer, F. R. and Comings, E. W., J. Chem. Eng. Data 5, 462(1960).

41

65. Touloukian, Y. S., Liley, P. E., and Saxena, S. C., “Thermal Con-ductivity Nonmetallic Liquids and Gases,” Thermophysical Prop-erties of Matter, Vol. 3, IFI/Plenum, New York, 1970.

66. Hanley, H. J. M., Gibbs, K. E., and Murad, S. J., Phys. Chem.Ref. Data, 6, 1167 (1972).

67. Bonscher, F. S., Shipman, L. M., and Yen, L. C., Hyd. Proc. 53 (2)107 (1974); 53 (4), 169 (1974).

68. “Key Chemicals Data Book – Benzene,” p. 23, ThermodynamicsResearch Center, Texas A&M University (1978).

69. “Perry’s Chemical Engineers’ Handbook,” 6th Ed., p. 247,McGraw Hill Inc., New York, 1984.

70. API Technical Data Book, Figure 12 B 1.1 (Oct. 1964).

71. Lenoir, J. M., and Comings, E. W., Chem. Eng. Prog. 47, 223(1951).

72. Hilrath, J. et al., NBS Circular No. 564 (1955).

73. Schaefer, C. A., and Thodos, G., Ind. Eng. Chem., 50, 1585 (1958).

74. Haran, E. N., Maitland, G. C., Mustafa, M., and Wakeham, W.A., “The Thermal Conductivity of Argon, Nitrogen and CarbonMonoxide in the Temperature Range 300-430 K at Pressures upto 10 MPa,” Ber. Bunsenges. Phys. Chem. 87, 657-663 (1983).

75. LeNeindre, B., Tufeu, R., Bury, P., and Sengers, J. V., “ThermalConductivity of Carbon Dioxide and Steam in the SupercriticalRegion,” Ber. Bunsen-Gesellschaft 77 No. 4, 262-275 (1973).

76. Sugden, S., “The Variation of Surface Tension. VI. The Variationof Surface Tension with Temperature and Some Related Func-tions,” J. Chem. Soc. 125, 32 (1924).

77. Stachorsky, K. M., “Surface Tensions of Liquid Mixtures,” Z.Elektrochem, 34, 111 (1928).

23

78. Weinaug, C., and Katz, D. L., “Surface Tension of Methane-Pro-pane Mixtures,” Ind. Eng. Chem. 35, 239 (1943).

79. Baker, O., Swerdloff, W., “Calculations of Surface Tension – 3:Calculations of Surface Tension Parachor Values,” Oil Gas J., 43,141 (Dec. 5, 1955).

80. API Technical Data Book, Ch. 10, Surface Tension.

81. Deam, J. R. and Maddox, R. N., “Interfacial Tension in Hydro-carbon Systems,” Proc. 48th Ann. Conv. GPA, Dallas, Texas,pp. 41-44, March, 1969.

82. Deam, J. R. and Maddox, R. N., “Interfacial Tension in Hydro-carbon Systems,” Proc. 47th Ann. Conv. GPA, New Orleans, LA,pp. 30-38, March, 1968.

83. Bagzis, L. D. and Maddox, R. N., “Calculating Surface Tension ofHydrocarbon Mixtures,” Proc. 49th Ann. Conv. GPA, Denver, CO,pp. 41-45, March, 1970.

84. Hadden, S. T., Hyd. Proc., October, 161 (1966).

85. Katz, D. L., Monroe, R. R., and Trainer, R. P., Pet. Tech., Sept.1943.

86. Quale, O. R., Chem. Rev., 53, 439 (1953).

87. Ritter, R. B., Lenoir, J. M., and Schweppe, J. L., Pet. Ref. 37No. 11, 225 (1958).

88. Carr, N. L., Kobayashi, R, and Burrows, D. B., Trans. AIME 201,264 (1954).

89. Adler, S. B., Hall, K. R., “Use Correlation for Oil Properties,”Hydrocarbon Processing, November 1985, pp. 71-75.

90. Private Communication May, 1997, R.N. Maddox and M. Mosh-feghian.

91. Soave, G., Chem. Eng. Sci., Vol. 27, No. 6 (1972), p. 1197.

92. Hankinson, R.W. and G.H. Thomson, AIChE J. 25: 671, 1979.

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