For a two-phase flow and in a specific reduced temperature (e.g. Tr=0.75), does the Redlich–Kwong (RK) equation of states predict a higher density ratio or Carnahan-Starling (CS)?
Could you introduce some references on your answers?
The RK EOS suffers from the same problems as all cubic equations of state, one of which is that the p~RT/(v-b) term increases much too rapidly as v approaches b. There is an excellent article discussing the various problems with cubic equations of state, which I think was written by G. G. Fuller. I have a copy of the paper somewhere, but I'm not sure where. I think the reference is G. G. Fuller, Ind. Eng. Chem. Fundam. 15, 254 (1976). The simplest way to greatly improve the accuracy in the compressed state is to make b a function of temperature and the acentric factor. I wrote a program that plots Pr vs. Vr, Tr vs Vr, Z vs. Pr, F vs. Pr, Hr vs. Pr, and Sr vs. Pr for 11 different equations of state as well as the generalized empirical formulation. You can see how these equations of state seem to predict the behavior of some properties better than others from comparing these plots, which is really convenient with this tool. I have put it on my web site with a link below.
http://dudleybenton.altervista.org/miscellaneous/eosplt310.zip
Dear Dudley J Benton,
very good program!
Are you involved in Equation of state yet?
Thanks.
Dear Ahad Zarghami,
I'm doing my PhD thesis on these issues: cubic equation of state and Carnahan-Starling-Desantis (CSD) equation of state. What is your interest on these equations? It would be nice to share our experience.
Although rarely mentioned, once you select an equation of state, you have defined the vapor pressure curve as well. Maxwell's Criterion requires that Psat*(Vg-Vf)=integral(P*dV) from Vf to Vg, because the Gibbs free energy of the liquid and vapor must be equal. Graphically, this is equivalent to recognizing that the area under an isotherm from Vf to where it intersects P=Psat and from this point to Vg must be the same, including where P
Many thanks Dudley ... your guidance is very helpful..
could you please direct me about the following :: based on your experiences,
1-by using which EoS I can approach density ratio around 1000 in Tr>0.7 ...
2- can we define/use any equation of state for water?? is it possible?
You can use many EOS for water, the official one is IAPWS, a multipararameter reference equation. To try it, you can use the ThermoC website; there you can also calculate tabvles and diagrams fro RK, CSRK, and many other EOS.
With cubic EOS, you cannot have good liquid densities and good virial coefficients; you alway have to sacrifice one for the other. Making b temperature-dependent should be done with caution; it practically always leads to artifacts like isotherm crossing at high pressures, as reported by Trebble and Bishnoi (M. A. Trebble and P. R. Bishnoi, Accuracy and consistency comparisons of ten cubic equations of state for
polar and non-polar compounds, Fluid Phase Equilib. 29 (1986) 465–474).
http://thermoc.uni-koeln.de/index.html
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