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# Pipe Wall Temperature during Steam Safety Valve Relief

## Pipe Wall Temperature during Steam Safety Valve Relief

(OP)
Hi

I need to calculate (or should i say I'm trying to calculate) pipe wall temperature for steam discharge line of a main steam system in a power plant. A safety valve releases this steam into discharge line in order to protect the system form over-pressure. This event occurs few times a year and lasts for short periods of time (max. 1 or 2 minutes).

Is there a way to calculate pipe wall temperature if a steam flows through pipe for let's say 40 seconds (or maybe 70 seconds; it doesn't matter, i want to know how the temperature of the pipe wall changes with time and also distance/length of the pipe).

The parameters of steam at the discharge pipe inlet are 500°C and 12 barg, flow is 160 t/h and the pipe is 25 m long.

I assume that the pipe wall won't reach this temperature because the steam flows through pipe for only 40 sec. (probably in reality this temperature will be significantly lower than 500°C)

### RE: Pipe Wall Temperature during Steam Safety Valve Relief

Depends on the pipe thickness. The pipe has a "thermal mass" whereby it needs to be heated up. The time to heat the pipe up can be calculated. You know the steam conditions and the time the pipe is subjected to the conditions therefore you can calculate the heat transfer to the pipe wall.

### RE: Pipe Wall Temperature during Steam Safety Valve Relief

In actual fact this is a fairly complex transient analysis whereby the temperature of the steel is affected by:

Mass / energy of steam
Temperature of steam
Mass of steel
convection / conduction / of heat from steam pipe increasing as temperature increases (or if insulated possibly ignore)
change in enthalpy of the steam along the pipe as energy transferred out ( might be negligible if there is a lot of steam / high velocity)

Why are you doing this? For a 25m pipe why not just assume it gets to 500C? The issue here is that you don't really have any control over the time period of the discharge. The fact that a safety relief valve is lifting " a few times a year" doesn't fill me with great joy and really should be dealt with at source. But the point remains - what happens if for some reason it releases one time for 5 times longer than you've calculated? Will it then fail??

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Pipe Wall Temperature during Steam Safety Valve Relief

(OP)
To be honest I'm trying to make stress analysis of this pipe a little easier for me, that's why I came up with this idea of calculating more "realistic" pipe wall temperature.

I did calculate the heat transfer form the steam to the pipe wall (in W/m), and from that I calculated that in 60 seconds 1 m of this pipe that is 12.5 mm thick get's from 20°C to almost 60°C.

### RE: Pipe Wall Temperature during Steam Safety Valve Relief

That's a pretty thick pipe for a vent line. What size is it? The bigger it is the lower the heat input for the same flow.

However the inlet pressure into a 25 long open ended pipe won't be 12 bar. You will get a pressure drop in the relief valve so that might impact your steam properties.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Pipe Wall Temperature during Steam Safety Valve Relief

(OP)
Excuse me, it's a 10" pipe - DN250 273x8 mm not 12.5mm. I was looking at another pipe dimension and I wrote here wrong thickness.

### RE: Pipe Wall Temperature during Steam Safety Valve Relief

Care to share how you calculated this, otherwise the thread is going a little cold ( to excuse the pun)...

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Pipe Wall Temperature during Steam Safety Valve Relief

I suppose I had two questions. Are you actually running into stress issues assuming full design temperature for the outlet line? And what's either the existing or considered pipe routing look like?

I'm not sure of all the calculations you've done so far but you've mentioned that you calculated 1 meter increasing 40°C after 1 minute while full design conditions could be up to 25 meters increasing 480°C. Now for a prolonged lift duration there will be a temperature gradient along the exhaust pipe due to outside air cooling it but this is a fairly drastic temperature difference between these two cases. Even though the relief device should never lift more than a minute, if it is allowed to lift for a prolonged period of time consider how much additional stress due to thermal expansion could exist between these two scenarios.

You may have already done it but I would recommend looking to see how the system handles full design conditions on the outlet piping. I may be just reiterating LittleInch's point but I don't know if going through a somewhat complex transient analysis to determine a temperature profile is going to make things easier regarding pipe stress. If you're going this route, find a reasonable pipe layout based on your experience, run at full design conditions, and then if there's a problem with stress introduce a temperature profile and reduce it till stresses are reasonable. After that possibly justify that the temperature gradient is realistic given some time constraints and air temperature and wind conditions.

Thanks,
Ehzin

### RE: Pipe Wall Temperature during Steam Safety Valve Relief

(OP)
Well,

first I calculated heat transfer rate using the inlet conditions of the steam in W/m of the pipe. I've attached an excel file i found on internet which I used for this purpose. Then i converted this heat transfer rate for 1m of the pipe and 60 seconds of time into energy that will be carried to 1m of pipe length in J.

Form equation Q=m*c*deltaT I calculated the temperature of my pipe after 60 seconds of steam flowing through it where:

m = mass of 1m of pipe 273x8 mmm
c = specific heat of steel
deltaT = temperature difference between two states of pipe wall temperatures i.e. start temperature and after 60 seconds

To be honest i did my pipe stress analysis using the 500°C pipe wall temperature (i found pipe route which keeps stresses below code required and also has minimum effect on silencer nozzle) but I'm doing this calculation to have more safety margin.

### RE: Pipe Wall Temperature during Steam Safety Valve Relief

Errr,

My calc on a fairly basic level is this.

1m of 12" 8mm pipe is 50kg
Heat capacity of carbon steel is 500J/kg/K, therefore 25000 J/ C rise.

1 m of pipe has an internal area of 0.86m2, therefore 1650 W/m/K
The delta C from steam to pipe is, at start, 480C, therefore heat transmission is 790kW - seems a bit big...

But that gives a temp rise in this pipe initially of 30C/second....

Now temperature and heat input will start to change as pipe temp goes up, but even so, it makes the 40C rise in 60 seconds look far too low.

Now whether the steam has enough heat capacity to achieve that is a moot point, but even so 40C in 60 seconds with 500C superheated steam going through what is a pretty thin pipe at near sonic velocity doesn't feel right to me

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Pipe Wall Temperature during Steam Safety Valve Relief

You're into heat transfer dynamics (pipe suddenly heating from within, but heating unevenly from inlet to outlet as the sudden inrush of steam cools and condenses as it flows through the relief valve outlet to the pipe outlet end); metallurgical dynamics (pipe losing strength but gaining flexibility as the pipe heats up towards saturation temperature - but probably approaching original full steam temperature near the valve itself); and stress dynamics (pipe suddenly heating when the steam hits it, then slowly cooling after the relief valve closes) PLUS the water/steam impact shock as the relief valve suddenly opens.

Not a good place for simplification. But, with so many unknowns, it is best NOT to treat some pretty 3D analysis as "perfect" just because it attempts to remove all of the unknowns and produces a pretty colorful picture. Of a physicist's theoretical world that may not reflect the real world.

Do the pipe heat expansion stress problem as if the pipe were insulated and at system temperature from relief valve outlet to exhaust pipe opening.
Do the stress analysis at the lowest pipe strength, highest pipe rigidity. (Those conflict, but it is conservative approach).

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