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 (C_p). The specific heat or heat capacity at constant pressure (C_p) 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 (C_v). This data is not so readily available and C_v value is much more sensitive to change in pressure and temperature in comparison to C_p.  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 (C_p), 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 = C_p / C_v ------------- (1)
 
For an ideal gas,
 
C_p - C_v = R ----- (2)
 
or
 
C_v = C_p - R ------ (3) 
 
Substituting (3) in (1) gives: 
 
γ = C_p / (C_p - R) -------- (4)
 
where:
 
γ = heat capacity ratio for an ideal gas, dimensionless
C_p = Specific heat or heat capacity at constant pressure, kJ / kmol-K
C_v = 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 = C_p / (C_p - (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 (C_p) to the heat capacity at constant volume (C_v). 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.
 
κ_mixture = Σ(y_i*κ_i)
 
where:
 
κ_mixture = heat capacity ratio of the gas mixture
y_i = mole fraction of the i^th pure component
κ_i = heat capacity ratio of the i^th 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.