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# Compressibility Factor And Ratio Of Specific Heats

4 replies to this topic

### #1 go-fish

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Posted 29 March 2012 - 08:10 AM

How do I find out Z factor and ratio of specific heats using HYSYS for relief valve sizing? I have a service comprising of a mixture of iso-butane and normal butane.

### #2 go-fish

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Posted 30 March 2012 - 08:23 AM

Let me add more details if it can help to answer my question.

For discharge area calculation, I need the Z factor and ratio of specific heat(k) at "relieving conditions".

I have calculated the Z factor from one of the excel spreadsheets from Mr. Ankur available in this forum. For 'k' value, I am not sure whether to use HYSYS value obtained by isochoric heating of vessel contents from normal to relieving pressure. Because this giving different k value depending upon if Vapor fraction is zero or vapor fraction is one. In reality, relief will be in vapor phase. What would be the correct approach?

### #3 sheiko

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Posted 31 March 2012 - 12:58 PM

I believe you should take time to study the standards API 520 and 521.

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Posted 31 March 2012 - 11:10 PM

2. If HYSIS gives you the vapor density at conditions then you can calculate the z-factor using the ideal gas law equation. Alternatively, rewrite the PSV sizing equation in terms of vapor density. In fact, the z-factor is used for calculating the density as defined by the universal gas law which is expressed in terms of pressure, temperature, MW and R.
3.Use the Cp/Cv ratio as given in the API Recommended Practice. However, for educational sake, you can calculate the Cp from enthalpy at two temperatures and the fact that Cp - Cv = R

Edited by S.AHMAD, 31 March 2012 - 11:16 PM.

### #5 paulhorth

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Posted 19 May 2012 - 12:48 PM

The relationship Cp - Cv = R is true only for an ideal gas. A mixture of n-butane and isobutane vapour is far from ideal.

Here is how I would suggest you find a value for k.
I assume you have a vessel containing isobutane and n-butane liquid mixture in equilirium with its vapour. Make a copy of your liquid stream in Hysys, set it to the relieving pressure (set point plus overpressure) and set its vapour fraction to zero. This gives the bubble point temperature. Now set the vapour fraction to about 0.01 and note the REAL Cp/Cv reported by Hysys for the initial vapour phase, which will be almost all isobutane.
Now set the vapour fraction to 1.0, this gives the dew point temperature, note the value of the real Cp/Cv.
The relevant Cp/Cv will be part way between these, reflecting the mixed vapour composition in the drum, which will depend on the temperature, but since you have isobutane and n-butane, I expect there will not be much difference, so you can use an average value.

A general method for finding the value of the true k value is as follows.
By definition, k for isentropic expansion = (ln(p1/p2))/ln(rho1/rho2) where conditions 1 and 2 are at the same entropy, covering the operating range of interest.To find this using HYSYS, make a Property Table with the first independent property being entropy fixed taken from the relieving condition, the second independent property being pressure ranging from 1 to 2,and the dependent property being density. Make the pressure intervals in the range as small as you like. Then just read out p1, p2, rho1 and rho 2, and calculate k.

Fortunately the relief valve sizing is not strongly sensitive to k, so some approximation will not make a big difference.You need to take care if your caalculated valve size is close to a standard size.

Paul