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Joule-Thomson Inversion Curves for Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) Equations of State

​
equation of state
SRK
PR
reduced temperature
T
r
1
reduced pressure
P
r
1
Throttling a real gas can sometimes result in a temperature decrease. If such is the case, the Joule–Thomson coefficient
μ=
∂T
∂P
H
is positive. This coefficient can be written as:
μ=
R
2
T
c
P
P
∂Z
∂T
P
,
where
R
is the universal gas constant,
c
P
is the constant-pressure heat capacity and
Z
is the compressibility factor. In order to estimate the value of
μ
, two equations of state are applied: the Soave–Redlich–Kwong (SRK) EoS and the Peng–Robinson (PR) EoS.
This Demonstration uses arc-length continuation to compute the Joule–Thomson inversion curve (i.e. the loci of the points, in the
P
r
-
T
r
plane, where
μ=0
). Here we choose propylene, but the program can be modified for any other pure component. You can set the value of the reduced pressure and temperature (i.e.
P
r
and
T
r
, respectively). This Demonstration will mark your choice by a green dot in the
P
r
-
T
r
plane. If your choice corresponds to a point inside the colored area, then the value of the Joule–Thomson coefficient is positive (see Snapshot 1); otherwise
μ<0
(see Snapshot 2). The inversion curve and colored region are both indicated either in red (for the SRK EoS) or in blue (for the PR EoS).
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