Maximum (ôchokeö) rate different at Single/two phase Choke flow

[silebi66]

Dear Professional engineer
Choke pressure is pressure at choke point divided by stagnation pressure (P0).
(Please see the attached file)
Refer from the graph, there is no flow at first Pb=P0. And, after Pb decrease, then flow begin. Pb get lower and lower, then flow gets higher and higher, eventually the maximum flow is reach. Then, Pb continue to drop, there is no changing in the flow.
My question is:
1. Why is the choke pressure ratio for two phase flow around 0.9, and choke pressure ratio for gas is around 0.6? For two phase flow, why is the graph chokes sooner? Ex. at 80 lb outside pressure (if inside pressure is 100lb), there is no effect in the flow.
Thank you very much.

 

[PaoloPemi]

you would need to estimate the speed of sound,
for natural gas I would suggest HEM model
and a suitable EOS as Peng-Robinson or Soave,
there are more complex models (than HEM) but
for usual calc's HEM is reasonably accurate,
select the proper EOS according the fluid,
for example IAPWS 95 would be required for water/steam,

to calculate the speed of sound for gas, liquid
or gas + liquid flows you need to calculate
volume and entropy + derivatives,

to avoid coding complex procedures I
use a process library which does all that
directly in Excel (PRODE PROPERTIES),

this is useful as you
can graph, for example, the speed of sound
at different conditions and see what happens,
in Excel there is the macro

=StrMSS(stream)

which returns the speed of sound for gas, liquid or
vapor+liquid mixtures with HEM method,
compare these results with your values,

instead if you wish to model a valve as isentropic
nozzle (rigorous procedure to simulate a PSV)
use the method ISPF() which includes several models
(HEM, HNE, NHNE etc.),
there is an Excel page which allows to compare results of
HEM vs. HNE or other models.