Pressure Drop in Vent

[Jersey72]

I'm routing a vent from a start-up valve for a Boiler to atmosphere on the roof. This start-up valve remains open and vents steam while the pipe is warming up and the boiler reaches operating condition. I was given 550F at 500 psig at 120,000 lb/h as design conditions for the steam. Just doing a pressure drop calculation using at 8" CS pipe I calculated roughly 12 psi which seemed okay. I was then asked about the pressure drop at 50psi (considering possible conditions during start-up) and found an 8" pipe, after I already routed it, created too great of a pressure drop in the system, due to increase in the specific volume. Apart from haggling about design conditions with the client, what is the accurate way to model the system. The steam doesn't flash to atmosphere after it leaves the Flow Control Valve. What specific volume do you use to do the calculation?

 

[SeanB]

If I read your post correctly you have 500 psig steam at the inlet to your control valve - is that correct? If so, what is the pressure drop across your valve at 120,000 lb/hr?

 

[Jersey72]

I wasn't given that info nor have I calculated it. The 120,000 lb/hr is a maximum flow rating for the Flow Control Valve so assumed to be fully opened. Assuming that the pressure is roughly 500 psi after the valve.

 

[katmar]

Although you must consider the pressure drop in the design of this pipe, it is not the point to start from. The situation you describe cannot occur in real life. You have assumed that you have 500 psig at the start of the pipe and a pressure drop of 12 psi. This makes the outlet pressure 488 psig. But in fact atmospheric pressure is 0 psig by definition. The extra 488 psig can't just disappear.

In fact what happens is that the pressure at the outlet of the pipe will be 0 psig or about 15 psia. The exit velocity head complicates things slightly and I will neglect it for now. Guessing the outlet temperature to be 450F, and taking the pressure as 15 psia, the density of your steam issuing from the vent will be 0.0277 lb/ft[sup]3[/sup]. If you are prepared to have a very noisy vent you could allow the exit velocity to be 400 ft/s. A flow of 120,000 lb/h at this density and velocity requires a diameter of 23.5 inches - say a 24" standard pipe.

Now that you know the required diameter of the pipe you can go back and check that you have sufficient pressure drop available. In this case the available pressure is far more than you need and it is not the limiting criterion.

Using an 8" pipe is going to force the exit velocity to be sonic and you will disturb your neighbors for miles around. And you will only get a discharge of around 24,000 lb/h.

I'm afraid this is a "back to the drawing board" situation. (Does anyone here remember drawing boards??).



Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[Jersey72]

If you connect the vent piping to a silencer located on the roof, do you still assume that your outlet conditions at the pipe are atmospheric.

 

[katmar]

The vent from the silencer will be atmospheric, but of course the inlet to the silencer (=end of pipe) will be a bit higher because of the pressure drop through the silencer. A silencer works by gradually slowing the velocity of the steam, and in order to get these lower velocities the pressure drop through the silencer has to be relatively low. I would guess of the order of 3 psi, but check with the silencer vendor/designer.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[Jersey72]

Is it wildly inaccurate to assume linear pressure drop through the pipe? If I have 500 psia at one end of a 237 ft. pipe venting to atmosphere, I can roughly assume 2 psi per foot of pipe. I'm trying to increase the pipe size as I get closer to the outlet in accordance with fluid velocity guidelines, and am assuming a linear drop throughout the pipe. Instinctively it seems as though the velocity gets faster towards the pipe outlet.

 

[KernOily]

You may be wildly inaccurarte assuming linearity but I can't say for sure. The velocity does increases as you get closer to the end because as the pressure drops, the specific volume goes up.

You need some type of simulator that can recalcluate the specific volume every so often (you define how often) as the steam travels down the vent pipe.

 

[insult2injury]

Starting with an 8" pipe and increasing the size downstream doesn't solve your problem of choked flow in the smaller diameter pipe.

I2I

 

[pleckner]

What equation(s) are you using to get your pressure drop? As you go down the pipe the steam accelerates and yes, the pressure drop will change, it is not linear.

For this system, you should be using the gas flow equations (compressible flow) and certainly not the incompressible flow equation. For simplicity I typically use the isothermal gas equation as it is just as simple to use as Darcy.

If you can get your hands on Crane TP410 there is an example problem that you can follow. It will show you how to use a simplified adiatatic gas flow equation, which for this system, is probably the more accurate way to go.

 

[katmar]

I agree with pleckner that you should be using the isothermal gas equations. It is vary rarely that I even bother to investigate the adiabatic situation because in practical terms it makes very little difference and in general the isothermal assumption is the conservative one (i.e. higher pressure drop). To properly apply adiabatic theory you need the ratio of specific heats at the flowing conditions and the uncertainty in this data can be considerable (if you can even find it).

But it is very interesting to consider the linear pressure drop model you have queried. Assuming a linear pressure drop is basically calculating the steam as though it were an incompressible liquid. This assumption also means you must have a constant pipe diameter for the entire length.

If I assume that you have 120,000 lb/h of steam flowing through 237' of 24" pipe, and I calculate it on the isothermal gas basis, I get a pressure drop of about 1.55 psi. This is very small, and is about 10% of the absolute pressure. If you read Crane 410 (or many other fluids handbooks) you will find a rule-of-thumb that says that if your pressure drop is 10% or less of the absolute pressure then using the Darcy incompressible fluid equation is reasonably accurate. So let's try it.

Using Darcy and the exit density I get a pressure drop of 1.44 psi. So maybe assumptions of linear pressure drop and incompressible flow are not so bad here. Basically you are trying to select between a 24" pipe and a 22" pipe and the difference between those pipes is much greater than the errors in using the incompressible assumption. As I said before, you are really selecting an exit velocity, rather than a pressure drop.

However, and its a big however, you most definitely cannot divide your 500 psi over the length and work on 2 psi/ft. This would force you into sonic flow conditions where assumptions of incompressible fluids with linear pressure drops simply do not apply. I would hesitate to use my isothermal based software under those conditions. Leave that stuff to the aeronautics boys. We don't work like that in process plants.

I would be very interested to know what inlet pipe flange size your silencer supplier has worked on. Do you have that information?

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[sailoday28]

katmar states(Chemical) 24 Jan 08 9:05
"I agree with pleckner that you should be using the isothermal gas equations."
Please note that for isothermal compressible flow, limiting conditions are not Mach=1, but Mach=1/sqrt(Cp/Cv)

Regards

 

[KernOily]

"Please note that for isothermal compressible flow, limiting conditions are not Mach=1, but Mach=1/sqrt(Cp/Cv)"

As far as I know this holds true for the ideal gas assumption only. This application is a significant enough deviation that you would be looking at errors in the tens of percents, methinks.

If I was doing this, I would use a simulator like Pipephase after I decided whether M is > or = 1. It continuously recalcs all properties all along the length of the pipe and uses the generalized energy equation to solve the problem. (No connection, just a satisfied user.) If you don't have that software, call up your neighborhood engineering contractor and pay him an hour to do this for you. It does not do supersonic flow though ( I wish it did...) and will not predict the formation of a shock.

 

[pleckner]

"Please note that for isothermal compressible flow, limiting conditions are not Mach=1, but Mach=1/sqrt(Cp/Cv)"

OK, so? We still talk in terms of choked flow when dealing with the Isothermal equations so I don't see the issue here?

 

[sailoday28]

The issue is that limiting flow does not occur at M=1, but at a different Mach number. That is sonic velocity does not occur at choked flow.

 

[Jersey72]

How would I verify that choked flow will not occur, if say I want to keep the first half of the pipe routing at 8", and then bump it up in the second half so that my exit velocity is reasonable. Choke flow occurs when you're pressure drop is greater than your starting pressure?

 

[4Pipes]

You should be using fanno flow equations in this situation. Isothermal is only applicable for "long" pipe at relatively low M and steady flow such that it is isothermal. Isothermal is definitely not applicable to high mach number lines - whatever process engineers might say or do. You will then be able to find whether or not it is choked.

 

[sailoday28]

4Pipes (Mechanical)
For Fanno line, with M approaching 1 how would one model the silencer? Can an equivalent L/D be used?
I might ask the same with isothermal flow as M aproaches its limiting number.

 

[4Pipes]

Sailoday,

M will only occur at internal choke points if there are any or at the pipe exit. Hence you need to start at the exit and work backwards. There is no direct solution.

I would suspect that the silencer pressure drop would very dependent on the silencer design. I would talk to the silencer supplier.