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# Heat Capacity Ratio (κ) Compilation From Hysys At Real Conditions Heat Capacity Ratio or Specific Heat Ratio has been discussed in many posts on "Cheresources". The heat capacity ratio is used for head calculations of compressors and for orifice sizing calculations for gas flow through control valves, relief valves and restriction orifices. Thus the importance of accurate value of the heat capacity ratio cannot be overemphasized enough. Today's blog entry makes an effort to provide heat capacity ratios at real conditions of pressure and temperature denoted as "κ", rather than the heat capacity ratio based on ideal gas conditions which can simply be obtained based on the specific heat or heat capacity at constant pressure (Cp). The specific heat or heat capacity at constant pressure (Cp) can be easily obtained from various open sources such as the "Nist Chemistry WebBook" and other chemical database available on the internet or other open source literature. The problem lies in obtaining the specific heat or heat capacity at constant volume (Cv). This data is not so readily available and Cv value is much more sensitive to change in pressure and temperature in comparison to Cp.  For ideal gas conditions calculating the specific heat or heat capacity ratio is a much simpler exercise since it requires only the specific heat or heat capacity at constant pressure (Cp), which is insensitive to changes in pressure and temperature of the gas in the narrow range of pressures and temperatures encountered for ideal gases. The following is the simplistic derivation of the heat capacity ratio for ideal gases:

Heat Capacity Ratio, γ = Cp / Cv ------------- (1)

For an ideal gas,

Cp - Cv = R ----- (2)

or

Cv = Cp - R ------ (3)

Substituting (3) in (1) gives:

γ = Cp / (Cp - R) -------- (4)

where:

γ = heat capacity ratio for an ideal gas, dimensionless
Cp = Specific heat or heat capacity at constant pressure, kJ / kmol-K
Cv = Specific heat or heat capacity at constant volume, kJ / kmol-K
R = Universal Gas constant expressed in energy units = 8.31447

If heat capacity or specific heat is provided in units of kJ / kg-K equation (4) gets modified as follows:

γ = Cp / (Cp - (R / MW)) --------- (5)

where:

MW = molecular weight of the compound

Wikipedia provides the following definition for the heat capacity ratio at the following link http://en.wikipedia...._capacity_ratio

The heat capacity ratio or adiabatic index or ratio of specific heats is the ratio of the heat capacity at constant pressure (Cp) to the heat capacity at constant volume (Cv). It is sometimes also known as the "isentropic expansion factor" and is denoted by γ (gamma) (for ideal gas) or κ (kappa)(isentropic exponent, for real gas).

Today's blog entry provides a spreadsheet compilation of the "κ" values for pure compounds or components at various conditions of pressure and temperature using the simulator Aspen HYSYS Version 7.3 and is mainly intended for those who do not have access to process simulators such as HYSYS. The data has been compiled using the "Peng-Robinson" equation of state (EOS) which is one of the most preferred EOS when dealing with hydrocarbons in the oil & gas industry. "κ" values for non-hydrocarbons such as CO2, H2S, N2 and Dry Air have also been provided using the same "Peng-Robinson" EOS.

Some odd or deviant values for "κ" have been observed at high pressures and temperatures while compiling the data from HYSYS. The same have been highlighted in yellow and corresponding ideal gas heat capacity ratios in brackets have been provided for these odd or deviant "κ" values.

When dealing with a gas mixture of pure components the law of proportions may be used with reasonable accuracy to estimate the "κ" values for the gas mixture at the given pressure and temperature.

κmixture = Σ(yii)

where:

κmixture = heat capacity ratio of the gas mixture
yi = mole fraction of the ith pure component
κi = heat capacity ratio of the ith pure component

This is probably the most comprehensive "κ" value compilation provided as an open source that the readers of "Cheresources" will find at real pressures and temperatures using a widely recognized process simulaton software such as HYSYS.

Hope this will be appreciated by all and I look forward to comments from the readers of my blog on this blog entry and the attached spreadsheet providing the "κ" value compilation.

Regards,
Ankur. twell
in addition to the excellent compilation of values provided by Ankur
you may consider also these sources which allow to calculate a number of properties including cp and cv

for properties of pure fluids there is a online calculator (based on REFPROP),
REFPROP includes very accurate models for pure fluids

http://webbook.nist....hemistry/fluid/

for properties of pure fluids and mixtures directly in Excel, Matlab etc.
there is a free version of Prode Properties,

http://www.prode.com/en/properties.htm

Prode Properties includes several EOS as Peng Robinson, Soave Redlich Kwong etc.
which give values close to Ankur's results Kazbek

Hi,

I,m trying to calculate flow of gas mixture (amount of gas realesed to flare) through globe valve.

As you said if,specific heat ratio k is for real gas and y is for ideal gas:

If for k value I found specific heat of mixture by κmixture = Σ(yii), how to do the same whith y ( for ideal gas)

as in my formula provided by valve manufacturer, it is in y(gamma) value  however I have doubt and I think I have to look for another formula with (k) value as it is for real gas.

Thanks. Trey

When sizing PSVs, don't use Cp/Cv at real conditions.  If you don't want to calculate the isentropic expansion coefficient, use the ideal K value (labeled Cp/ (Cp-R) in Hysys) and set the Z factor to one.  This is in API 521.

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