Annular Flow of Compressible Fluid 1

[sloquick]

Anyone have experience with flow equations for natural gas in a circular pipe flowing around an innerduct (annular flow). Want pressure drop for given flowrate with initial pressure of 10 to 60 psig. Pipe is 1 to 6" IPS plastic, cast iron or steel. Innerduct is plastic 1/8" to 1" CTS.

 

[Flareman]

This sounds like a classic case to use the hydraulic diameter of the annulus.
Find the area of the annulus to calculate the velocity, but use the hydraulic diameter to find the friction coefficient and friction losses.
Hydraulic diameter = 4 x (wetted flow area / wetted perimeter). Then treat it as if it's an independent pipe.
For a true circular concentric annulus, the hydraulic diameter works out to the width of the annular space.
You'll need a formula for friction factor which uses the variable surface roughness characteristics of your different materials. I use "colebrook" which needs an iterative solution but you can input the hydraulic diameter into the relative roughness section.
The rest is standard hydraulics. For the DP I suggest the isothermal compresible flow. There are innumerable reference on this site to papers but, like others, I'd start with the Crane publication 410.

That all sounds too simple !!
If I've misunderstood your question please say so.

 

[sloquick]

Simple is a relative term. Thanks Flareman.

 

[zdas04]

The equation I've found most often in wellbore models is
[[ID{outer)+OD(inner)]^2*[ID(outer)-OD(inner)]^3]^(1/5)
You use the result of this equation just like it was an actual diameter of a conduit. It gives pretty good results for flow and friction calculations.

 

[sloquick]

Thanks zdas04. Our limited flow tests also produced results that were quite a departure from those predicted using the standard hydraulic diameter. We'll give your approach a shot and see if we can close the gap. By the way, do you use this same diameter to calculate friction factor? Some type of equivalent roughness as well?

 

[zdas04]

Yeah, I pretend that the "D(eff)" is a real "D" and use it for everything. Including Darcy Friction factors (it is a bit of a stretch accepting that the outside surface of the inside pipe is just as smooth as the inside, but measurements have shown it to be pretty close).

"Accurate" is such an elusive term in vertical multi-phase flow which is what most gas-field wellbore flow tends to be.

 

[sloquick]

zdas04. In the case of plastic innerduct and main, the assumption is probably not that much of a "stretch". Yeah, I imagine your applications are pretty complex. You seem capable of meeting the challenge. Thanks for your helpful responses.

Kevin