choked flow pressure profile in vent lines

[will48]

I'm looking at a vessel vent line, which will be used to manually depressure a vessel containing light natural gas at 100 barg to an atmospheric vent header. The line is equipped with a restriction orifice and downstream of the RO passes via several collection headers, all of increasing size, e.g. 3" line to 8" sub-header to 24" main header. The main header for the purposes of my calc is assumed initially at atmospheric pressure, and I'm estimating the built-up backpressure to the RO. The gas flow is limited by the RO, but can reach sonic velocity in one or more of the downstream lines. Assuming critical flow across the orifice (i.e. flowrate not affected by downstream pressure), what happens to the pressure at the sudden line size increases?

Do I have:
(a) max orifice flow, with pressures dictated by sonic flow limit, and pressure discontinuity at the line size change? Or,
(b) a continuous pressure curve (albeit 'lumpy') with the orifice flow limited by sonic flow in any section?

In other words:
(a) flowrate is dictated by orifice; sonic flow at end of each increasing line section; pressure discontinuous at line size increases
(b) pressure is continuous, flow is much reduced due to sonic velocity in the max line size

 

[Latexman]

Have you seen faq378-1864? It is pertinent.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

 

[Latexman]

The answer is (b). All the pieces make up a system that obeys the rules/laws of compressible flow.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

 

[casflo]

First you must be sure if the RO has critical conditions. If the RO has a square-edge hole and the relation between the thickness of the plate to the hole diameter is approximately 5 or less, the RO has no critical conditions.
If the RO has critical conditions, could be also critical conditions in the section changes of the vent pipe, but the flow is fixed by the RO if the vent pipe imposed a back pressure at the RO outlet less than its critical pressure.

 

[MortenA]

Casflo - where did that law come from? I would think the equation by API 520 (sec 5.6.2.4) would be better suited for determining if the RO is choked or not?

 

[zdas04]

Casflo,
Like MortenA, I think that you are better off looking at API 520 than API 14.3 on this one. The choke area of a PSV is far less than 5d and they do actually give you choked flow. It looks like you are confusing "permanent pressure loss" with "choked flow", a common error.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[casflo]

The PSV valves have smoothly convergent nozzles instead square-edge orifices, for this reason the API 520 considers an isentropic expansion and they may have chocked flow.
But the plates with square-edge orifices have not this phenomena.
For example see in the Crane TP 410 pages A-20 and A-21 the difference of the net expansion coefficient Y for ROs and nozzles. The nozzles have a limit in the pressure ratio as a consequence of the critical pressure and the ROs have not.
You may see also the following papers about this matter:
- "Sizing orifices for flow of gases and vapors". P. C. Tung and M. Mikasinovic. Chemical Engineering, March 1982.
- "The flow of saturated water through throttling orifices". M. W. Benjamin and J. G. Miller. Transactions of the ASME, July 1941.
- "Low pressure differential discharge characteristics of saturated liquids passing through orifices". T. J. Rohloff and I. Catton. Transactions of the ASME Vol 118, September 1996
casflo