Critical Pressure, Maximum Pressure Drop Across Valve, Sonic Velocity, Maximum Exit Velocity

[bengoali]

Hello Guys,

Recently join this community as I saw some really helpful posts. I've come across a control valve problem which has really high flow requirements.

The process conditions are as follows:
[ul]
[li]p1 = 10.3 barg[/li]
[li]p2 = 1 barg[/li]
[li]Q = 2,000,000 kg/hr[/li]
[li]k = 1.403[/li]
[li]M = 28.97 kg/kmol[/li]
[li]Z = 1 [/li]
[li]T = 65 degrees C[/li]
[/ul]

Based on k, the critical pressure ratio (p*/p0) is 0.5279. deltaP exceeds the critical pressure ratio therefore the fluid is supercritical and at sonic velocity.

The issue here is I believe the wrong valve has been selected which has an inlet diameter of 584mm and an outlet diameter of 510mm.

At the sonic velocity which is 369 m/s, the maximum flow rate possible (choked flow), should be limited to the flow rate possible through the 510mm restriction?

Using the equation:
Q = Cd * A * SQRT(k*rho0*P0*((2/k+1)^((k+1)/(k-1))))
Q = Flow rate (m^3/s)
Cd = discharge coefficient (used 0.9)
A = area (m^2)
k = specific heat ratio
rho0 = density at temperature, pressure and compressibility (kg/m^3)
P0 = inlet pressure (Pa)

I calculate this to be approx 1,570,000 kg/hr which is less than the flow rate required however at 584mm its approx 2,050,000 kg/hr?

If this is correct,the best option here would be to increase the size of the outlet to 584mm also?

Furthermore, I calculated the velocity at the outlet if the flow rate is 2,000,000 kg//hr:

Q = 2,000,000 kg/hr
A = 0.292 m^2 (using outlet diameter of 609.6)
rho2 = 2.07kg/m^3 assuming T2 = T1

This gave me a really high outlet velocity of 919.55 m/s. The valve outlet is attached to an expander which increase to 56".

Will this velocity be achievable on the outlet? Or will it be limited to M = 1 i.e. 369m/s?

Furthermore, if the velocity at the valve exit is M=1, will the expander continue to increase the velocity? (Following the principle of De Laval nozzle where outlet velocity can exceed M=1) or will it be subjected to Fanno flow?

Also, considering deltaP exceed critical pressure, what would the pressure at the valve outlet be? Would it be 5.43737 barg and then this down to 1 barg at the outlet of the pipe?

If any clarification is needed, please ask.

 

[LittleInch]

Err, are you sure about all those numbers??

Especially density which I can only assume is at your p2 pressure? or at atmospheric pressure (0 barg)

you don't seem to be looking at what is happening inside the valve itself which will be a smaller size than the inlet and outlet.

What is the CV of the valve when fully open? Or if this is a control valve it shouldn't be more than 75 or 80% open

This does seem to be a very large quantity trying to go through a relatively small valve.

What is this stuff? Why are you going from 10 bar to 1 barg through a valve?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[davefitz]

I suggest you use the valve flow calculation defined in the ISA handbook of control valves. That calculation corrects for oblique shaock waves and also predicts the noise levels.

Thermodynamically it is correct that the max flow is limited by the minimum open area which is 510 mm in this case, but other cosntraints ( including oblique shock waves) . Per safety codes, there is also a workplace limt on noise, so the type of vale geometry must be modified to limit noise, so it is best to use the ISA method.



"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick

 

[georgeverghese]

Pressure at the pipe outlet would be 1bar abs, not 1barg.
To work out the backpressure (exit pressure) on this control valve, start from the pipe outlet and work backwards till you get to the CV exit.

 

[bengoali]

After the expander there is a chamber. Based on the other process data, I do believe its barg and not bar abs.

We use a software which uses the IEC 60534 standards to calculate the required CV for flow cases, noise predictions and also the CV of the valve.

Noise isn't much of a concern in this application.

The CV for this case is 12945 and the CV of the valve is 16221.

However I'm concerned on the outlet of 510mm. Will this not limit the flow coming out of the valve?