Modeling an Adiabatic Expansion (EES)

[Ainadak]

How would one model an isentropic (reversible) adiabatic expansion using thermodynamic software in order to determine isentropic work? What I am looking for is an actual pressure-volume curve for the isentropic expansion of a gas.


Approach using EES:

1) Start with a known gas state/scale (Mass, Volume, Pressure, Temperature, Enthalpy, Entropy, etc.)
2) Update gas volume by a small increase in volume dV
3) Work done = Pressure * dV
4) Keep entropy constant
5) Recalculate new gas state based on the new Specific Volume (Volume/Mass) and Entropy
6) Repeat until final state has been reached.

Summing the work done in this method results in significantly less work (~80%) than is possible through isentropic expansion. The max isentropic work is calculated through
Wmax = Mass * (h_initial - h_final)

Even with very small step sizes (thousands of steps), this approach doesn't work. Can anyone shed some light as to why these work values don't match up?



Code:

Procedure AdiabaticExpansion(P, T, P_final : Work_max, Work)
Vol=1
v=Volume(CarbonDioxide,P=P,T=T)
s=Entropy(CarbonDioxide,P=P,T=T)
h_initial=Enthalpy(CarbonDioxide,P=P,T=T)
Mass=Vol/v
Vol_step=1/10000
Work=0

repeat
Vol:=Vol + Vol_step
v:=Vol/mass
Work_step:=(P)*Vol_step
Work:=Work + Work_step
P:=Pressure(CarbonDioxide,v=v,s=s)
until (P <= P_final)

h_final=Enthalpy(CarbonDioxide,P=P,s=s)
Work_max=mass * (h_initial - h_final)
End

 

[sailoday280]

For the non flow process described, dU=-pdv or dh=vdp
Regards

 

[MikeClay]

In Hyssys/Unisim I just run a case study using the turboexpander with a 100% efficiency.

--Mike--

 

[chemlite]

for a pure fluid you may consider to use a mollier chart, google for turbo expanders for additional information,
as alternative, as suggested by others, you may consider a simulator or a process library,
I have PRODE PROPERTIES which allows to solve the operation directly in EXCEL

 

[sailoday280]

Whether

 

[sailoday280]

Whether flow or non flow, delta h is the integral of vdp. With flow, change of kinetic energy should also be considered for the isentropic process under consideration
Regards