Transfer line sonic velocity 3

[mrobles1942]

Hi
At present I'm involve in a revamp study of a refinery vacuum unit. One thing that I must check is if the transfer line is a hydraulic limitation.
In order to evaluate the sonic gas velocity in the transfer line I've used this mathematical expression:

Vs(ft/s)=68,2 • (K•P/dens.)^1/2

It is supposed that the result should be the maximum velocity ( or vacuum column throuput) due to the size of the line.
However, the velocity that I got using experimental data (real flowrate) is higher that the theoretical sonic velocity.
Somebody could give me a explanation about that?
Is it right the mathematical expression that I use to evaluate the sonic velocity?
Are there another way to evaluate the sonic velocity?
I would appreciate very much some help

Thank you

 

[Latexman]

V[sub]s[/sub] = (kgRT)[sup]1/2[/sup] = (kg144P’/[ρ])[sup]1/2[/sup] = 68.1(kP’/[ρ])[sup]1/2[/sup]

k = c[sub]p[/sub]/ c[sub]v[/sub]
g = 32.2 ft/sec[sup]2[/sup]
R = individual gas constant = 1545/M
M = molecular weight
T = [sup]o[/sup]R
[ρ] = density in lb/ft[sup]3[/sup]


Good luck,
Latexman

 

[Latexman]

P' = psia

Good luck,
Latexman

 

[25362]

Mrobles1942. Can you show us your calcs., in particular the density used ?

 

[mrobles1942]

The mathematical expressions provided by Mr Latexman are practically equal to the used by us.Therefore the results are also identicals.
Nevertheless the real value is greater :
(1) (2) (3)
Sonic speed (m/s) 116 115.5 148

(1)From our mathematical expression
(2)Mr Latexman mathematical expressions
(3)Real calculated value (Based experimental data)
The gas density that we use is :0.05 lb/ft3

Mathematical expresion:
Vs(ft/s)=68,2 · (K·P/dens.)^1/2
Datas:

K (= Cp/Cv) 1,008
P 1,554 psia
Gas.dens. 5,03E-02 lb/ft3
Vs 380,59 ft/s ( 116,00 m/s)


Pipe diameter 16 in
Pipe diameter 406,4 mm

Thanks

 

[Latexman]

One of the assumptions made in the above equations is the gas/vapor behaves as an ideal gas. The temperature has not been stated, but if I assume it's around 520 R, the MW is estimated at 180. If this fluid is coming out of/going to a condenser, it may not behave as an ideal gas. What is T, MW, and Z, the compressibility? Could non-ideal gas behavior be the problem?

Good luck,
Latexman

 

[Latexman]

Take a look at an FAQ I wrote; it's faq1203-1293.

If you have a more rigorous equation of state (EOS) for your fluid, it is exactly what you need. Make a spreadsheet with the equations given, add the logic for your EOS to give the isentropic change in temperature as a function of pressure , set d[sub]nozzle[/sub] = 16", and find where G[sub]n[/sub] goes through a maximum numerically. It'll take some trial and error to make the maximum G[sub]n[/sub] coincide with your known pressure, but it can be done by adjusting the stagnation pressure and temperature, i.e. the first P[sub]n[/sub] and T[sub]n[/sub] in the numeric integration.

If coming up with the isentropic change in temperature of your EOS is onorous, use the adiabatic change in temperature.

By the way, you should be able to do this in Aspen or another simulator, if you already have a model of the physical and thermodynamic properties.



Good luck,
Latexman

 

[25362]

The temperature is important because it affects the thermal cracking of the atmospheric residue in a direct (inverse) relation to its Watson K factor. The higher its value the lower the incipient cracking temperature, even under vacuum.

Assuming no velocity steam is injected in the heater tubes, significant cracking leads to the formation of light ends, changing the vapors' density which would affect the estimation of the velocity of sound. Steam injection would also increase the value of K=Cp/Cv and reduce the density.

Consider these factors and recalculate the sound velocity.

 

[25362]

I may add that the general approach for well-designed and operated "dry" vacuum towers is to assume 0.2 mass% of light ends on feed. Their MW is assumed to center at about C7.

 

[reena1957]

Dear Mrobles1942,
25362 has hit the nail on the head. Can you pl tell us the basis for the gas composition/density? Also tell us how you measured the experimental sonic velocity?
Best wishes

 

[EmmanuelTop]

One of the things that is often being overlooked is an asumption of 100% L/V equilibrium at the heater coil outlet, i.e. an ideal two-phase flow. By using wash zone heat balance equations, you can (at least) try to calculate the exact % of feed vapor content - the amount of vapor superheating compared to perfect equilibrium, in other words. These results, then, you can use in transfer line hydraulic calculations. I think you will be quite surprised with the results.
Cracking reactions, as 25362 pointed out, are very significant factor influencing K/RO terms in the above equations. I would also like to find out how did you measure the true transfer line velocity.

Regards

 

[CJKruger]

mrobles1942,

Vacuum heater transfer line design is difficult.

1) There are significant flashing in the transfer line. Flashing depends on pressure drop and on heavy end characterization.

2) It is 2-phase flow and no exact correlation for choke/critical flow exist.

3) Most people use the gas phase choke flow equation, with or without correction for the liquid phase.

4) During design, it is sufficient to use the gas phase sonic equations, and simply limit the velocity to say 80% of sonic.

5) For troubleshooting or revamp, you are not that lucky. Velocities above 100% of gas phase sonic velocity are possible.

6) It is difficult to decide what happens in reducers and expanders. An expander is where you will probably see sonic velocity first due to the pressure to velocity conversion.

And these are just the process issues. Then there are a host of mechanical, stess, layout, expansion, etc issues.