16 replies to this topic

[nrxbra001]

Hi All,

 

I have a very interesting question:

 

I am performing a valve calculation to determine the mass flow passing through a particular line. This line contains off gas material and is connected to a low pressure flare header (about 4KPa (A)) which is open to atmosphere. The pressure upstream of the valve is 135 KPa (A). The line is 3" and is about 20 m from the end of the valve to the header (12" line).

 

This is where it gets tricky for me, the valve is fully open. There will be some pressure loss through the valve seat and such, but what is a reasonable outlet pressure from the valve? If I assume a 30 KPa loss through the valve, the outlet pressure is 105 KPa. That implies a loss of 101 KPa 20m of line? That seems unlikely as the this is a gas and the only loss is frictional.

 

The other assumption I can make is that the pressure on the outlet of the valve is similar to the header, let's say about 10 KPa. But this means i get a pressure drop of 125 KPa over an open valve? That seems very excessive.

 

I'll appreciate any response.

[shan]

"The other assumption" is correct.  The flare system back pressure is determined by the flare tip pressure drop curve and line pressure loss.

[fallah]

Hi,

 

By (A) you mean absolute? If so, is the header under vacuum? What is the valve type?

 Please upload a simple sketch with mentioned additional info...

[Pranay]

The flow in this type of situations is typically limited by fluid mach number.  If the valve is not designed to eat-up all the pressure drop, then the fluid (vapor) flow thru the pipe will increase to a point where mach number exceeds 1.0 at some point in the line.  You can use adiabatic compressible pressure drop equation to determine the flow at which mach number equals to one for known straight pipe length.  A good reference book is Ron Darby's chemical engineering fluid mechanics.  Perry also has equations to help you perform adiabatic pressure drop calculations.

[Zauberberg]

Is it a globe control valve in question? If yes, then there is a defined Cv for any % of valve opening. Now you have to define pressures upstream and downstream of the valve, and the equation is complete and without unknowns.

 

This is an iterative process. The higher the flow, the higher is the pressure drop in the piping upstream and downstream of the valve. So - assume flow, calculate pressure drop(s), then see if the valve passes that much flow at given % opening (=Cv) and pressures upstream/downstream of the valve. Do you get more flow? Then increase the flow. Do you get less flow? Then decrease the flow. Repeat the procedure till you have everything matched.

[nrxbra001]

"The other assumption" is correct.  The flare system back pressure is determined by the flare tip pressure drop curve and line pressure loss.

This is what I assume, but is that much pressure drop across an open valve realistic?

[nrxbra001]

Hi,

 

By (A) you mean absolute? If so, is the header under vacuum? What is the valve type?

 Please upload a simple sketch with mentioned additional info...

Sorry I did mean absolute, but I didn't add atmospheric pressure. So the pressure upstream of the valve is 135Kpag and the header is at 4 Kpag. This is an equal percentage control valve.

[nrxbra001]

The flow in this type of situations is typically limited by fluid mach number.  If the valve is not designed to eat-up all the pressure drop, then the fluid (vapor) flow thru the pipe will increase to a point where mach number exceeds 1.0 at some point in the line.  You can use adiabatic compressible pressure drop equation to determine the flow at which mach number equals to one for known straight pipe length.  A good reference book is Ron Darby's chemical engineering fluid mechanics.  Perry also has equations to help you perform adiabatic pressure drop calculations.

 

 

Is it a globe control valve in question? If yes, then there is a defined Cv for any % of valve opening. Now you have to define pressures upstream and downstream of the valve, and the equation is complete and without unknowns.

 

This is an iterative process. The higher the flow, the higher is the pressure drop in the piping upstream and downstream of the valve. So - assume flow, calculate pressure drop(s), then see if the valve passes that much flow at given % opening (=Cv) and pressures upstream/downstream of the valve. Do you get more flow? Then increase the flow. Do you get less flow? Then decrease the flow. Repeat the procedure till you have everything matched.

Thanks for the reply,

 

I have considered sonic flow to try and make sense of it. the critical pressure ratio is at 0.54 for this gas, which means the critical pressure is at about 73KPag. Now considering the header pressure is at about 4 KPag and that we are dealing with a gas and not a long length of pipe (small frictional losses); can the pressure realistically be that low on the outlet of the valve?

 

I guess my question is really can we have a pressure drop if about 70KPa over a wide open valve?

Edited by nrxbra001, 21 March 2015 - 12:09 PM.

[Zauberberg]

Valve is simply an adjustable orifice. It is the same as if you are asking a question "can pressure really drop from 100 barg upstream to 1.5 barg downstream of the orifice, during depressurization to flare header of a vessel that operates at 100 barg?"

[katmar]

As stated by Zauberberg, this type of problem has to be solved iteratively. But for a first estimate it is useful to make a few reasonable assumptions so that the number of variables to iterate becomes manageable. So, let us assume that the flow through this valve is small compared with the overall capacity of the flare header. This allows us to assume that the end pressure is fixed at 4 kPag. Secondly let us assume that the piping upstream of the valve is designed to give a small pressure drop and that the pressure immediately upstream of the valve is fixed at 135 kPag or 235 kPaa.

Now we have a much simpler problem. We know the start and end pressures, and we know (or at least you do) the geometry of the valve and pipe. The only unknown now is the flow rate, and this is what we can find by iterating. In any iterative solution you need to determine what is the variable that you will be changing. In this case the variable that we will guess and test is the pressure immediately downstream of the valve. If we know (or assume) the pressure downstream of the valve then we can calculate the flow through the valve and we can also calculate the flow through the 3" pipe that connects the valve to the header. We keep guessing values for this pressure until the flows through the valve and pipe are equal - as they must be.

Once you have a value for the flow rate you can test your initial assumptions and you might have to change the values for the end pressures - the 135 kPag and 4 kPag. And then you repeat the above iterative procedure.

One possible wrinkle is if the flow through the valve is choked. You have indicated that your critical pressure ratio is 0.54. This means that the downstream pressure of the valve must be 0.54 x 235 = 127 kPaa or greater to avoid choking. This is probably a good starting point for our iterative search for the valve's downstream pressure. We calculate the flow through the valve with an upstream pressure of 235 kPaa and choked flow, and also calculate the flow through the 3" pipe with a 23 kPa differential pressure (=27-4).

There are 2 possibilities here. If the flow through the valve is more than the flow through the pipe then we know that we have guessed too low a pressure for the valve's downstream pressure and that we do not have choked flow. Increase the guessed pressure and recalculate.

The second possibility is the more interesting one. If the guess of choked flow means that the flow through the valve is less than through the pipe then the usual iterative process would say we need to lower the guessed pressure. But lowering the downstream pressure will not increase the flow through the valve (because it is choked). What would happen in practice is that a shock wave would form downstream of the valve and the flowrate through the combined valve and pipe would be determined by the choked flow capacity of the valve (since the pipe has a higher capacity).

Edited by katmar, 22 March 2015 - 04:33 AM.

[shan]

Sure, the pressure drop is realistic.  There is no pressure drop limit for a valve, if the valve building material is strong enough. 

[Pranay]

As mentioned by Zauberberg and katmar this is a iterative calculation.  I've attached a sample calculation here with three different valve sizes.  

 

I've used discharge coefficient method to estimate the flow thru valve assuming isentropic flow.  You can use Cv method if you have Cv vs % valve open curve.  The results depend entirely on the valve design and the information provided in my spreadsheet is for demonstration purpose only. 

 

Few notes:

You will not be able to access the pressure drop formula as I've used an in-line function for the calculation.  Using isothermal pressure drop model will yield slightly different results and I would NOT recommend isothermal model for this purpose. Isentropic nozzle flow equations are from perry.  I'm providing the calculation on as-is basis only as I've developed it only for demonstration.

 

I hope this helps.  Comments and suggestions are welcome.

Attached Files

•  Valve Plus Line Pressure Drop.xlsx   24.73KB   78 downloads

Edited by Pranay, 23 March 2015 - 06:17 PM.

[Bobby Strain]

Pranay,

      I can't add to your post. But I would like to know how you put the inline function into Excel. I recognize it as VBA, but it's not found in the customary VBA Module. Is this something that is in versions later than 2007? My search yields nothing. Maybe you can enlighten me.

 

Bobby

[Pranay]

Mr.Strain,
The in-line function is custom user defined, developed in VB or VBA. You will need *.xlam or *.xll file to use the function which I've not provided. However, the concept is to calculate pressure drop in the line using fluid properties and pressure downstream of the valve.

[Zauberberg]

Quite illustrative example, Pranay. Here goes a star from me for your post.

[Pranay]

Quite illustrative example, Pranay. Here goes a star from me for your post.

Thank you for the kind feedback Mr. Zauberberg.

[nrxbra001]

Hi all,

 

Thanks for your input, i did the calculation as suggested and have got results which indicate choked flow conditions, To prove this I managed to get some plant readings which looks like this:

 

Upstream pressure at 110 KPag

Downstream pressure at 7.34 KPag

I simulated the composition of the gas on ASPEN properties and got a value for k (Cp/Cv) of 1.28.

 

From this value of K i get the critical pressure ratio as 0.54 for an ideal gas, which implies that an outlet pressure less than 59.4 KPag will result in choked conditions (which is currently the case).

 

Is there anything physical that i can do to verify that we're choking. I know in certain valves we do get very noise/vibration but is there any other check?