Flow through back-pressure regulator

[Eltron]

Hello, All. I have a question that on the surface seems simple, but I think I'm making it more complicated than it should be.

Suppose I have a system that flows helium through a reactor at 1000 psig. The helium flow is delivered through a mass flow controller. The reactor pressure is kept steady by a back-pressure regulator. The exhaust after the back-pressure regulator is vented directly to ambient pressure. So here's the question: after the system has reached equilibrium, will the flow coming out of the back-pressure regulator (at ambient pressure) be equal to the flow into the system (via the mass flow controller)?

It seems to me that the flow through the back-pressure regulator will be choked due to the high dp, but my internal conflict is that, if the regulator is working properly, the internal orifice size will constantly be adjusting to keep the system pressure at 1000 psig. Am I making this too complicated, or is it as simple as flow in equals flow out?

Appreciate the help.

 

[TD2K]

It's as simple as mass in = mass out + accumulation in the reactor. Your mass controller will be maintaining a fixed flow into the reactor. The backpressure regulator will adjust itself as needed to maintain the reactor pressure which means, on an average basis, it must vent the same amount of helium you are adding (I'm assuming no helium leaves with the product).

Over the short term, there can be some differences in the two flows as reactor temperatures, levels, etc change (if that's a possibility) as those would affect the accumulation term but over the long haul, the accumulation term would be minor.

 

[Ashereng]

mass in = mass out + accum/losses

vol in <> vol out + accum/losses

Flow is usually in volumetric units. I would expect the flow rates to be different, but the mass rates to be the same. Your inlet flow is at 1000 psig. You are venting at 0 psig.

"Do not worry about your problems with mathematics, I assure you mine are far greater."
Albert Einstein
Have you read FAQ731-376 to make the best use of Eng-Tips Forums?

 

[proinwv2]

The important issue is that the back pressure regulator responds only to pressure.

With the inlet at 1000 psig, the flow assuredly will be choked. Very common with gas valves, especially blowing down to atmosphere.

BTW it will be noisy!!!

PAUL

Paul Ostand

http://www.ostand.com

 

[moltenmetal]

Your analysis is correct- if the regulator is sized properly, it will vary its orifice area to keep pressure constant such that mass in equals mass out. Except of course that the back pressure regulator may deliver the entire rate of helium flow required to maintain 1000 psig in the reactor when it's closed! Getting it to stay helium leak-tight so that it does an adequate job of regulation may be a challenge depending on the regulator's design. 1000 psig is a lot of driving force for something as "slippery" as helium. If the feed flow of helium is low, the challenge will be to keep the leakage through other paths low enough to ensure that mass in = mass out.

 

[edthefanman]

Obviously this is based on the Cv of the BPR. If the incoming feed is either very high or very low, you may have an issue.

If the BPR is sized to match incoming - which it usually is, and the Cv value is pretty high, even just cracking the BPV will cause you to lose pressure in the vessel, hence adding more, hence losing more etc etc. If the Cv is lower, then you should be OK, as just cracking the valve only allows out a small bit. The BPR regulates constantly, so if you are constantly adding, then it will operate in direct response to the amt added.

Obviously you will end up with choked flow, and after a while...a requirement for a new BPR. And as mentioned, it will be loud.