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# Pressure Increase in Thermal Relief

## Pressure Increase in Thermal Relief

(OP)
Hello Everybody,
I have a relief device protecting the tube side of a shell & tube heat exchanger(Process Water Heater).
The Fluid Composition is as follows:-
Tube Side - Water(90 psig normal operating, max. 150 psig) heated from 50 to 60ºC.
Shell Side - 35#Steam.
Relief Device Set @ 150 psig.
The only relieving case for the relief device is Hydraulic Expansion which  considers the tube side to be liquid-full & blocked-in while continuous flow of 35#Steam to the shell side.
The relief rate can be calculated using the API 521 Equation:- gpm = BH / 500 GC.

My question is :- Is their any way I can calculate the increase in pressure on the Tube Side based on the increase in temperature due to hydraulic expansion ?

Please do let me know if their is a equation/graph  or book or reference I can use to calculate the pressure increase.
Thanks,
Parimal

### RE: Pressure Increase in Thermal Relief

My guess is that you are assuming that the water in the tube may never reach the design pressure of the pipe and therefore why would you want to install a relief valve?

My understanding is that thermal expansion in a closed system can drastically raise the pressure.  Here is an article that may help...

http://www.chemicalprocessing.com/Web_Fi...

Analyses show that for 2-in. Schedule 40 carbon-steel or stainless-steel pipe, trapped water will reach an ultimate pressure of 1,200 psig with only a 30°F temperature rise or 40 psi/°F, not the 50 psi/°F suggested by Equation 7. Typical compressibility values are given in Table 2.

In your case you could potentialy raise the temp from 50C (122F) to 35psig steam temp of 281F - difference of ~160F...40*160 = 6400psi???  Of course this all depends on the piping setup.  But take a look and I think you'll find out why API 520/521 doesn't include that pressure calc...in nearly all cases the expansion rate is large enough to increase pressure that a relief is always necessary.

### RE: Pressure Increase in Thermal Relief

(OP)
Hi nalmeter,
Thanks for your response. The article you referred to is very neat & very informative.That helped.

parimal

### RE: Pressure Increase in Thermal Relief

parimaldesai:

nalmeter is very correct in his analysis of your system.  There is no need to waste time or effort on trying to find out the increase in pressure on the Tube Side based on the increase in temperature due to hydraulic expansion.  If you effectively block in the cooling water and continue feeding steam to the shell side, you are going to develop hydraulic liquid water expansion that could astronomically exceed 150 psig in the tube side -- but only if it is not relieved safely.

Although the hydraulic volume increase (which causes the high pressure) is only going to be possibly a cm3 or less, the resulting pressure is still very high.  This will happen while sensible heat is transferred to the blocked-in water and is approaching the saturation point of the resultant system.  A period of latent heat will follow (assuming you haven't relieved by now) and subsequently steam could start to be generated if a sufficient thermal driving force still exists between the 35 psig steam (280 oF) and the now-hot cooling water.  You will probably never get to the steam generation because of the increased pressure and increased saturated temperature of the water, but all this is academic when put into the reality that you have an over-pressurization scenario.

Since you say you have a 150 psig set pressure PSV on the tube side, this will "pop" and relieve the expansion hot water when the developed hydraulic pressure reaches 150 psig.  You are protected at that stage.  If your PSV is 3/4 to 1" size, this should suffice.  You don't need formal engineering calculations to prove to OSHA that you have sufficient liquid expansion capacity in the PSV.  Such is the smallness of the relieved stream.  This has already been calculated countless times in the past with the recognized results that the size of the expanded liquid is negligible and not worthwile calculating for the sake of safely protecting the scenario.  But the point is: why waste your time in trying to calculate the resultant pressure?  It will only get to 150 psig and relieve under your system.  That's the important point - the rest is academic.  The author of the recommended article says it very well: "the value of operating experience far outweighs that of quantitative analysis".

Art Montemayor
Spring, TX

### RE: Pressure Increase in Thermal Relief

(OP)
Art Montemayor,
Thank you for the response & I totally agree with you on the point that the liquid expansion case is already calculated countless times & why waste time in trying to calculate the resultant pressure.
Its just that I'm a junior process engineer & my RV sizing work is audited by the senior engineers & one of the senior engineer asked me to calculate the increase in pressure along with the temperature rise & thats how I ended up posting my question. Anyways, the article was really great & I learned a lot from it & I also got my answer.I passed the article on to my senior engineer.
I appreciate your time & help.
thanks,
parimal

### RE: Pressure Increase in Thermal Relief

parimaldesai:

Thank you for explaining the real situation.  It helps me feel better that you are on top of the situation and recognize exactly what you are dealing with.  As long as the safety ramifications are taken care of, I'm sure you are happy and can deal with your senior engineer's whims and fanciful trips into theory.  It appears you can show your seniors a thing or two in real-world practical engineering.

Art Montemayor
Spring, TX

### RE: Pressure Increase in Thermal Relief

I understand what you both are saying.  I too (recently) just went through the same calculations and discovered (once again) that I have to install a small relief for every valid blocked in heat exchanger case.  I also know what your senior engineer is looking for, Parimal, since I recently was working with a design firm and all my work was checked the same way.  I think you on the right thinking track!  Keep it up.

Nick
Augusta, GA

### RE: Pressure Increase in Thermal Relief

Refer to API 521, sec 3.14, Hydrualic expansion.

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