Choke P2 Calculation

[rkm502]

I am trying to solve a choke problem. I would like to solve for the downstream pressure if all other variables are known. I am collecting data from flow meters and pressure transmitters and want to compare the measured downstream pressure to the calculated downstream pressure to determine if the choke has eroded. I am trying to accomplish for both sonic and sub-sonic conditions.

The best equation I have located for the sub-sonic condition is attached. Does anyone know how to solve this equation for P2?

Or any other equation to accomplish the same?

Thanks for your help.

 

[Latexman]

Even after a good deal of algebra, I'm not sure you'd ever get it in an explicit form for p_dn. I'd put the equation into Excel and use Solver.

Before a different equation could be recommended, I'd like more details on the process. Having a flow coefficient in the equation, implies there is a constriction of some kind, but what type?

If you have the measured downstream pressure as stated, why not solve for Q_sc and compare that to the measured flow? I suspect you'd need to change the actual flow rate to the flow rate at standard conditions. or vice versa, but that seems much easier that solving for p_dn.



Good luck,
Latexman

 

[rkm502]

Thanks for the reply. I didn't realize excel had a solver.

I am measureing the pressure upstream/downsteram of a choke. I am trying to determine how much the choke has erroded by comparing the measured downstream pressure to the calculated downstream pressure.

The problem with trying to do this with using the flow rate, is the pressure cut is across a choke, not an AGA orifice plate - so I think using the pressure is the way to go.

Can you point me in the right direction no the excel solver.

Thanks again.

 

[Latexman]

On my Excel 2003, Solver is an Add-In. If you have not installed it, go Tools/Add-Ins and check mark Solver Add-In. If you don't see it, you might need your installaion CD. After adding it, just go Tools/Solver.

Good luck,
Latexman

 

[hacksaw]

you down stream pressure is a function of the discharge conditions, so measuring the back pressure does give you some idea of the flow. That's is where the problems start since you may not have the downstream conditions.

 

[FOURe]

For isentropic flow, the following compressible flow equations should be valid:

Tt / T = (1 + M^2(k - 1)/2)

pt / p = (1 + M^2(k - 1)/2)^(k/(k-1))

ht = (h + v^2/2)

Tt = (T + v^2/(2cp))

In my opinion, for known inlet condition such as stagnation temperature and pressure and knowing that that flow gets choked (M = 1), it should not be difficult to find out outlet conditions such as static temperature and pressure.

One can always reverse the problem and start with static temperature and pressure for the choked flow and try to find out inlet conditions such as stagnation temperature and pressure.

For outlet conditions, one can always use the ideal gas state equation pv = RT and density = 1/v to determine the mass flow rate at choked conditions -- m = density * v * A.

In my opinion, A needs to be known.

The above is valid for choked/sonic conditions. Similar approach can be taken for subsonic conditions.

Here is a URL for an online nozzle calculator that can speed up isentropic compressible flow calculations:

http://www.engineering-4e.com/calc5.htm

I do hope that my input will be of some help to you.

http://www.engineering-4e.com

 

[FOURe]

Here are a few plots when it comes to the nozzle operation -- such plots just present general performance trends for the above equations when dealing with isentropic and ideal nozzle expansion for subsonic and sonic compressible flow conditions:

​

Note: The nozzle performance plot should be a general plot even though it makes a reference to the inlet stagnation conditions of 1,500 [K] and 10 [atm] when the working fluid is air!

http://www.engineering-4e.com