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Modeling an Adiabatic Expansion (EES)

Modeling an Adiabatic Expansion (EES)

Modeling an Adiabatic Expansion (EES)

(OP)
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

RE: Modeling an Adiabatic Expansion (EES)

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

RE: Modeling an Adiabatic Expansion (EES)

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

--Mike--

RE: Modeling an Adiabatic Expansion (EES)

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

RE: Modeling an Adiabatic Expansion (EES)

Whether

RE: Modeling an Adiabatic Expansion (EES)

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

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