3 replies to this topic

[adw07]

Hi all,

I am looking at adiabatic de-pressurisation of a vessel using the Peng-Robinson Equation of State.

Using a time-step model, at each time interval an iteration loop needs to solve for temperature, equating the molar enthalpy of the system.

I am unsure whether I can use the equation of state itself to find the enthalpy (If so - which equation?) or whether I would have to use specific heat capacity correlations to do this.

Any help appreciated.

[S.AHMAD]

Hi,
I have not done any adiabatic expansion using enthalpy balance. The method I normally used is using the adiabatic equation:

PV^k = cosntant

And simplified equation of state (EOS)

PV = ZRT

You can simply replace this equation with PR equation of state, but the procedure will be the same namely

1. Using initial conditions (P1 and T1), calculate V1 using EOS (for PR EOS, need trial and error and have more than 1 value of V - need to choose the right one that is very close to V1 = zRT1/P1)
2. Calculate V2 using adiabatic equation
3. Compute T2 using EOS since P2 and V2 are known

You can estimate the value of T2 using:

T2/T1 = (P2/P1)^m

Where m = (k-1)/K

K = CP/CV , ratio of specific heat

It would be interesting to compare the 2 method.

[adw07]

Hi, thank you for your response. I should have mentioned above that I am considering vessels containing vapour and liquid, and so upon de-pressurisation some liquid will evaporate.

I am wondering if it is possible to apply the method above to this two-phase situation, although I do not know how it would account the the latent heat of vaporisation.

I had originally thought if the PR EOS can be used to calculate enthalpy, then the molar enthalpy for the mixture as a whole should be constant throughout, and an enthalpy balance can be used to find the new temperature.

[S.AHMAD]

The calculation is then very complex for two phase flow.
Generally, the steps is as below:

1. Assume temperature
2. Determine k (equilibrium constant)) for each component. Can use vapor pressure, initially. then use PR EOS subsequently
3.Do flash calculation (vapor -liquid Equilibrium)
4. Do enthalpy balance (Enthalpy in - Enthalpy out = 0)
5. If enthalpy balance requirement is not met repeat Step 1

The above calculation is tedious. I normally use HYSYS or PRO-2 to do the job for us.

You can INTEGRATE the specific heat correlation to get the enthalpy of components or if temperature variation is small, you can assume the specific heat constant.

Best regards and good luck