2-Dimensional Temperature Distribution in Pipe

[retropmas]

Looking to install a 2" nozzle in the spent wash oil sump on a VPS. The nozzle will function as a Nitrogen bubbler type lower LC connection with a diaphragm seal between the nitrogen and the fill fluid. The problem is that I'm not sure what temperature to tell the instrument guy to spec the fill fluid for. The spent wash oil is normally around 725F but can get up to 750F, and apparently the best the instrument guy can do is a fill fluid rated for 650F. I've heard that a rule of thumb is 100F temperature drop/ft for this scenario but I was hoping someone could help me actually calculate this.

From the generalized energy equation in cylindrical coordinates or from shell balances I can come up with -1/r * d/dr(rq_r)+dq_z/dz = 0

I could solve this if it were a regular differential equation, but the partial differential has really stumped me.

Anybody have any idea where to go from here, or even an article or anything discussing this, I couldn't find anything this specific.

 

[Compositepro]

I'm not sure I understand your question. It appears that you are using a N2 bubbler to sense level of wash oil at 725F. Then you are measuring the N2 pressure through a diaphragm seal. This diaphragm is usually part of the differential pressure sensor, which must be located pretty far away from any 725F heat source (and which would be insulated). The fill fluid and DP sensor should never see more than 150F in any reasonable installation.

 

[retropmas]

The seal is not all that far away from the process fluid. The nozzle is 9" long, then a valve, flush ring, and finally the seal. The whole apparatus is roughly 2ft from the vessel. The nozzle is filled with Nitrogen, but all the metal will readily conduct heat all the way to the seal with very little resistance. I was thinking to cage, not insulate the apparatus in hopes that enough heat will be lost via convection on the outside of the nozzle that the temperature at the seal will be <650. Hence the above equation for heat flux in radial and axial directions for an annulus.

 

[Compositepro]

You may find this useful.

http://www.idc-online.com/technical...entation/Differential pressure meters_nel.pdf

Large temperature changes in your seal fluid may also cause problems due to changes in volume/density.