09-19-2021-0704 - Lee-Kesler Method 1975 ; Goff–Gratch equation 1946 ; correlation proposed to estimate the saturation water vapor pressure at a given temperature. Thermodynamic models Atmospheric thermodynamics ; Arden Buck equation

 The Lee–Kesler method ^[1] allows the estimation of the saturated vapor pressure at a given temperature for all components for which the critical pressure P_c, the critical temperature T_c, and the acentric factor ω are known.

Equations[edit]

with

 (reduced pressure) and  (reduced temperature).

Typical errors[edit]

The prediction error can be up to 10% for polar components and small pressures and the calculated pressure is typically too low. For pressures above 1 bar, that means, above the normal boiling point, the typical errors are below 2%. ^[2]

Example calculation[edit]

For benzene with

• T_c = 562.12 K^[3]
• P_c = 4898 kPa^[3]
• T_b = 353.15 K^[4]
• ω = 0.2120^[5]

the following calculation for T=T_b results:

• T_r = 353.15 / 562.12 = 0.628247
• f⁽⁰⁾ = -3.167428
• f⁽¹⁾ = -3.429560
• P_r = exp( f⁽⁰⁾ + ω f⁽¹⁾ ) = 0.020354
• P = P_r * P_c = 99.69 kPa

The correct result would be P = 101.325 kPa, the normal (atmospheric) pressure. The deviation is -1.63 kPa or -1.61 %.

It is important to use the same absolute units for T and T_c as well as for P and P_c. The unit system used (K or R for T) is irrelevant because of the usage of the reduced values T_r and P_r.

References[edit]

1. ^ Lee B.I., Kesler M.G., "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States", AIChE J., 21(3), 510-527, 1975
2. ^ Reid R.C., Prausnitz J.M., Poling B.E., "The Properties of Gases & Liquids", 4. Auflage, McGraw-Hill, 1988
3. ^ Jump up to: ^a b Brunner E., Thies M.C., Schneider G.M., J.Supercrit.Fluids, 39(2), 160-173, 2006
4. ^ Silva L.M.C., Mattedi S., Gonzalez-Olmos R., Iglesias M., J.Chem.Thermodyn., 38(12), 1725-1736, 2006
5. ^ Dortmund Data Bank

See also[edit]

• Vapour pressure of water
• Antoine equation
• Tetens equation
• Arden Buck equation
• Goff–Gratch equation

Categories: 

• Thermodynamic models

https://en.wikipedia.org/wiki/Lee–Kesler_method

The Goff–Gratch equation is one (arguably the first reliable in history) amongst many experimental correlation proposed to estimate the saturation water vapor pressure at a given temperature.

Another similar equation based on more recent data is the Arden Buck equation.

Historical note[edit]

This equation is named after the authors of the original scientific article who described how to calculate the saturation water vapor pressure above a flat free water surface as a function of temperature (Goff and Gratch, 1946). Goff (1957) later revised his formula, and the latter was recommended for use by the World Meteorological Organization in 1988, with further corrections in 2000.^{[citation needed]}

The current 2015 edition of the WMO Technical Regulations (WMO-No. 49) however states in Volume 1, Part III, Section 1.2.1, that any formula or constant given in the Guide to Meteorological Instruments and Methods of Observation a.k.a. CIMO-Guide (WMO-No. 8) shall be used, and this document only contains the much simpler Magnus formula (Annex 4.B. – Formulae for the computation of measures of humidity). Regarding the measurement of upper-air humidity, this publication also reads (in Section 12.5.1):

The saturation with respect to water cannot be measured much below –50 °C, so manufacturers should use one of the following expressions for calculating saturation vapour pressure relative to water at the lowest temperatures – Wexler (1976, 1977),^[1][2] reported by Flatau et al. (1992).,^[3] Hyland and Wexler (1983) or Sonntag (1994) – and not the Goff-Gratch equation recommended in earlier WMO publications.

Experimental correlation[edit]

The original Goff–Gratch (1946) experimental correlation reads as follows:

where:

log refers to the logarithm in base 10

e^* is the saturation water vapor pressure (hPa)

T is the absolute air temperature in kelvins

T_st is the steam-point (i.e. boiling point at 1 atm.) temperature (373.15 K)

e^*_st is e^* at the steam-point pressure (1 atm = 1013.25 hPa)

Similarly, the correlation for the saturation water vapor pressure over ice is:

where:

log stands for the logarithm in base 10

e^*_i is the saturation water vapor pressure over ice (hPa)

T is the air temperature (K)

T₀ is the ice-point (triple point) temperature (273.16 K)

e^*_i0 is e^* at the ice-point pressure (6.1173 hPa)

See also[edit]

• Vapour pressure of water
• Antoine equation
• Arden Buck equation
• Tetens equation
• Lee–Kesler method

References[edit]

• Goff, J. A., and Gratch, S. (1946) Low-pressure properties of water from −160 to 212 °F, in Transactions of the American Society of Heating and Ventilating Engineers, pp 95–122, presented at the 52nd annual meeting of the American Society of Heating and Ventilating Engineers, New York, 1946.
• Goff, J. A. (1957) Saturation pressure of water on the new Kelvin temperature scale, Transactions of the American Society of Heating and Ventilating Engineers, pp 347–354, presented at the semi-annual meeting of the American Society of Heating and Ventilating Engineers, Murray Bay, Que. Canada.
• World Meteorological Organization (1988) General meteorological standards and recommended practices, Appendix A, WMO Technical Regulations, WMO-No. 49.
• World Meteorological Organization (2000) General meteorological standards and recommended practices, Appendix A, WMO Technical Regulations, WMO-No. 49, corrigendum.
• "WMO Guide To Meteorological Instruments and Methods of Observation (the CIMO Guide)". 2014. WMO-No. 8.
• Murphy, D.M.; Koop, T. (2005). "Review of the vapour pressures of ice and supercooled water for atmospheric applications". Quarterly Journal of the Royal Meteorological Society. 131 (608): 1539–65. Bibcode:2005QJRMS.131.1539M. doi:10.1256/qj.04.94.

Notes

1. ^ Wexler, A. (1976). "Vapor pressure formulation for water in range 0 to 100°C. A revision". Journal of Research of the National Bureau of Standards Section A. 80A (5–6): 775–785. doi:10.6028/jres.080a.071.
2. ^ Wexler, A. (1977). "Vapor pressure formulation for ice". Journal of Research of the National Bureau of Standards Section A. 81A (1): 5–20. doi:10.6028/jres.081a.003.
3. ^ Flatau, P.J.; Walko, R.L.; Cotton, W.R. (1992). "Polynomial fits to saturation vapor pressure". Journal of Applied Meteorology. 31 (12): 1507–13. Bibcode:1992JApMe..31.1507F. doi:10.1175/1520-0450(1992)031<1507:PFTSVP>2.0.CO;2.

External links[edit]

• Vömel, Holger (2016). "Saturation vapor pressure formulations". Boulder CO: Earth Observing Laboratory, National Center for Atmospheric Research.
• Free Windows Program, Moisture Units Conversion Calculator w/Goff-Gratch equation — PhyMetrix

Categories: 

• Atmospheric thermodynamics

https://en.wikipedia.org/wiki/Goff–Gratch_equation