8 replies to this topic

[mrbabu]

I need to calculate isothermal compressibility for liquid phase in a natural gas mixture at conditions close to critical point, I have selected the SRK package (C1 > 85%) , calculated values show a large difference from those found in literature at low pressures for similar mixtures and I fear there is a problem, could you suggest a way to verify the results ?

[ankur2061]

mrbabu,

Can you upload a screen shot of your simulation along with composition and conditions for us to understand better. From your description it is difficult to provide a meaningful response to your query.

Regards,
Ankur.

[mrbabu]

Ankur,
I am calculating (liquid) isothermal compressibility for the mixture
Methane    84.5
Ethane    7
Propane    3
nButane    1.0
iButane 0.3
nPentane 0.2
nHexane 0.05
nOctane 0.05
Carbon Dioxide    1.1
Nitrogen 2.1
Hydrogen sulphide 0.7

@ 223 K, 75 Bar , SRK package

[ankur2061]

mrbabu,

I checked your data in HYSYS and I am getting a Z-factor (compressibility) of 0.4263 for the vapor phase and 0.2994 for the liquid phase. At the pressure and temperature conditions mentioned the natural gas mixture co-exists as liquid and vapor (liquid fraction: 0.6628 and vapor fraction: 0.3372) since the conditions are close to the critical point.

To my knowledge when modeling supercritical fluids using a simulation software the property package that is recommended is BWRS or Lee-Kesler-Plocker. Maybe somebody more knowledgable than me on modeling of supercritical fluids can recommend a better property package while modeling.

Hope this helps.

Regards,
Ankur.

[marchem]

mrbabu,
to verify your results you may download Prode Properties (from www.prode.com),
with your mixture and SRK Properties calculates for liquid isothermal compressibility

0.004154 (1/Bar) at 223 K AND 75 Bar.a
0.00010276 (1/Bar) at 223 K and 1 Bar.a

as you see the first value (@75 Bar) is much higher than second (@atm), that may depend from several factors as operating in retrograde region , different liquid compositions etc.
Prode exports analytical derivatives of volume so you can compare values, also with Properties you are able to get liquid (and gas) isothermal compressibility directly in Excel at different conditions with the macros
=EStrLIC(stream,t,p)
=EStrGIC(stream,t,p)

[marchem]

to answer Ankur's comment I compared the values of density and isothermal compressibility calculated with BWRS, LKP, SRK, PR, it is interesting to note how isothermal compressibility show variations much larger than the density,

feed composition (see mrbabu post)
Methane 84.5
Ethane 7
Propane 3
nButane 1.0
iButane 0.3
nPentane 0.2
nHexane 0.05
nOctane 0.05
Carbon Dioxide 1.1
Nitrogen 2.1
Hydrogen sulphide 0.7

isothermal flash at 223 K 1 bar.a
composition liquid phase calculated with SRK + BIPs
Methane 0.010
Ethane 0.0134
Propane 0.0427
nButane 0.0957
iButane 0.0178
nPentane 0.131
nHexane 0.1808
nOctane 0.5052
Carbon Dioxide 0.000775
Nitrogen 0.000040
Hydrogen sulphide 0.00152


liquid density (Kg/M3)
(BWRS) 727.35
(LKP) 728.083
(SRK) 733.830 (with Peneloux)
(PR) 718.404 (with Peneloux)


isothermal compressibility
(BWRS) 0.00005387
(LKP) 0.000101
(SRK) 0.000102
(PR) 0.00007394

isothermal flash at 223 K 75 bar.a
composition liquid phase calculated with SRK + BIPs
Methane 0.79
Ethane 0.092
Propane 0.0486
nButane 0.019
iButane 0.00549
nPentane 0.00427
nHexane 0.00117
nOctane 0.00131
Carbon Dioxide 0.0129
Nitrogen 0.0151
Hydrogen sulphide 0.0093


liquid density (Kg/M3)
(BWRS) 288.697
(LKP) 291.454
(SRK) 288.696 (with Peneloux)
(PR) 302.105 (with Peneloux)


isothermal compressibility
(BWRS) 0.004154
(LKP) 0.00588
(SRK) 0.004154
(PR) 0.00376

[mrbabu]

thanks marchem, useful information,
if I remember correctly the isothermal compressibility is defined as
-1/V * (dV/dP)T
since 1/V is the density which decreases (1Bar->75Bar) by a factor 700/300
the remaining contribute, the term (dV/dP)T must have a large variation,
is that correct ?

[marchem]

Prode Properties exports (I mean you can easily access the function from Excel or other software as Macro)

=EStrLIC(stream,t,p)
=EStrGIC(stream,t,p)

these calculate isothermal compressibility -(dV/dP)T / V at different conditions for liquid and gas phases

=EStrLVE(stream,t,p)
=EStrGVE(stream,t,p)

these calculate volume expansivity or thermal expansion coefficient -(dV/dT)P / V at different conditions for liquid and gas phases


in addition there are methods for calculating gas, liquid and solid volume (with specified composition and conditions) with derivatives vs. pressure, temperature and composition

StrVv(stream,....)

to answer your question, you can easily calculate

(dV/dP)T = isothermal compressibility * Volume

and for the cases evaluated the resulting values are in agreement with your hypothesis

[mrbabu]

thanks,
I appreciate the help.