Using DePriester Chart and Given one of mole fractions ($z$), pressure and temperature we can acquire K-values for that properties and bubble and dew properties.

Now there are sometimes that we get some K's and using the summation of $y/k$ we get some quantities that are not 1, like 0.9 or 1.2. My question is about those values, are they showing some physical property?

If I wanted to calculate the dew point pressure at a given temperature and I take arbitrary pressures (including the dew point pressure) I get the following results.

[p] = psi    sum of y/k
- - - - - - - - - - - - 
   100         0.828
   126         1.000
   150         1.174

Do the values for the pressures above and below the dew point pressure have a physical meaning?

For example, showing us that we are in two-phase, SH vapor or SC liquid region? Or are they just showing there isn't VLE with that given property?

  • $\begingroup$ Could you give an example of where this was done? I have a hunch where you are going with this. $\endgroup$
    – idkfa
    Mar 19 '16 at 7:54
  • $\begingroup$ @idkfa Ok an example,we have mole fractions and temperature, and we want dew pressure, so we take two arbitrary pressures and calculate summation of y/k , which y=z because we are in dew point,and k earned by DePriester,so if we try this summation in 100psi we get 0.828 and if we try it in 150psi we get 1.174 , and finally if we try 126psi we get 1 and thats the dew pressure,i wanna know about those 1.174 and 0.828,do they give us some physical signs about which regions are we in,by that pressure? $\endgroup$
    – Mo Samani
    Mar 19 '16 at 9:07
  • $\begingroup$ These numbers came from somewhere, it would have been nice if you'd provided the calculations. And please make sure to include important information in the question body. $\endgroup$
    – idkfa
    Mar 25 '16 at 12:38

You can represent K as $K_i = \frac{p_i^{sat}}{p}$ for an ideal mixture using Raoult's law.

This equation directly yields the correspondance of $K$ and $p$. If the pressure is below the dew point pressure $K_i$ will be larger. Hence $\frac{z_i}{K_i}$ will be smaller and subsequently the sum over it.

What this tells you is

$p$ yields $\sum \frac{z_i}{K_i} < 1$ pressure is below dew point pressure

$p$ yields $\sum \frac{z_i}{K_i} > 1$ pressure is above dew point pressure

Note: This is for a fixed temperature.

Alternatively you can make the same deductions with $K_i = \frac{y_i}{x_i}$ and the knowledge that at dew point the first drop of liquid forms.


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