Thermal Relief - test of relief assumptions

[Bill3752]

I have done several a bunch of RV calcs recently where thermal relief protection was the controlling case. I would like to get critical feedbackon some assumptions. For simplicity assume a cooling water system. I have been calculating the expansion coeficient using the delta temp/sp vol between operating and max temp.

For the more narrow case of a dead headed pump (i.e. infinite energy input), I have been using the saturation temp at the Ps/P1 to perform the expansion calcs. The essentially means that the motivation results due to the vapor pressure of the water.

However, I would like to test my themodynamic assumption that this relief is at saturation temperature. The only other "process" that I can envision is that liquid expansion would cause pressure to increase, but since this is a non-compressible fluid that would not make total sense.

Please give me your ideas.

 

[dcasto]

In a pumping system, how can you get more pressure than what the pump can put up in head, unless you have a check valve on the suction?

 

[djack77494]

Bill,
I think you are not properly identifying your situations and may be misusing the term thermal relief (= thermal expansion?) I typically use this term to refer to situations where I have a fluid "blocked in" or trapped in a fixed volume. Energy then moves into the trapped fluid, often just heat transfer from ambient or solar gain, etc. If we're talking about a vapor, pressure increase is negligable in every case I've seen. If we're starting with a liquid, my first point is throw away the thought that a liquid is non-compressible. (You use this term as if its volume can never change.) In fact, introducing energy into a fixed volume liquid filled system can generate enormous internal pressures. As the liquid's temperature increases, it tries to expand in accordance with its thermal coefficient of expansion. The liquid phase volume readily changes with temperature changes (albeit by a modest amount). It is much less responsive to volume changes caused by pressure. Think about it - it totally makes sense.
Doug

 

[Bill3752]

dcasto, thanks for the comment. I have actually run into two "pump/thermal" situations. In one, under dead headed conditions, the tdh is above the set point; since the pump is deadheaded, one moves up the pump curve to "obtain" the correct flow rate at relieving conditions. Under these conditions I have been assuming that the well subcooled material (water in most cases) will be relieved at Ps. In this case I assume subcooled liquid is relieved, and therefore there is little flashing. So I design for liquid relief.

Your thoughts on this approach? What would you assume for the relief temp?

 

[Bill3752]

djack, thanks for your insightful feedback. Actually we are in agreement. I am calculating the coeficient of expansion for each of these cases, and have seen numbers as high as .0007 (7 times the published numbers at ambient conditions!) as we are using very high process conditions. Referring to my last post to dcasto, this brings me to the second case. When the TDH is less than the set pressure (hence no flow) I have been computing the energy input into the system from the pump, and assuming that all of that energy is converted into increased temp (therefore expansion). big pumps = big energy = big temp changes = big expansion.

My question then becomes "starting with a subcooled liquid, and putting heat into the process, how would you calculate the relief temperature"? The obvious choice seems to be the saturation temp at the relief pressure. However, I am asking whether thermodynamically you feel I could reach the relief pressure before reaching the saturation temperature.

Thanks again for your thoughts.

 

[lizking]

If you are truly blocked in (both discharge side and suction side valves are closed) and the pump remains running, I would use normal operating temperature plus 10-20 degree increase. See API 521, fifth ed., 5.14.4 for calculation of cubic expansion coefficient for liquid thermal relief. You would then estimate the time it takes for the pump heat input to raise the temp to saturation. Then a judgment decision: is time long enough for operator intervention? If not, then RV must be sized for boiling liquid flow (2-phase).

 

[dcasto]

First, I wouldn't design the piping in a pump where deadhead would exceed MAOP.

Next, if it can and the piping would just be barely over the next pressure clas, I'd have a PSV on the discharge back to suction that can handle the full flow at the pump curves where the pressure exceeds MAOP.

Next, if you assume pump can deadhead or recirculate and build up heat, then you would assume that the energy put into heating the liquid and vaporizing it would be (100%-pump effiency in %) * HP at that point on the curve. That energy would go into the vaporizing of the fluid at the worse case scenerio.

 

[djack77494]

I basically agree with what dcasto has to say. However, I hate to run a pump PSV back to the suction header; better to return to the suction vessel. Also, in a case like this, I would prefer to use a modulating PSV, which functions an aweful lot like a control valve.

Regarding Bill's response to my earlier comment, for a completely liquid filled system that you block in, you could theorize that relief could be required almost immediately. Once isolated, any heat results in increased temperature = liquid expansion. Initial relieving temperature would then be initial liquid temperature. I don't really think that's realistic, but I can't put a different lower limit on relieving temperature. Can you?

 

[Bill3752]

djack, you are hitting on my issue - putting number on the relief temp that makes sense (I am arguing with myself re: the assumption is saturation temp).
Based on your earlier comment,and comments from lizking, I believe I will take one of the cases I have worked up and estimate the line volume, then assume 1st law thermo and estimate how fast the temperature (therefore expansion rise) might be and ask the question "is it likely that plant will catch". If yes, then I will assume a subcooled liquid.

 

[CMA010]

To obtain the relief temperature of a thermal relief case you can calculate which temperature increase you need to reach relief pressure (you know dP). You can use normal operating temperature or maximum normal operating pressure as initial temperature.

When you have heat input from a pump you'll first have thermal relief(s)(liquid expansion), followed by a vapour relief when the medium reaches saturation temperature.

 

[Bill3752]

Thanks for all of your comments. Based on your input, I looked at an example case, assuming that the heat generated from the pump was converted 100% into thermal heat and that the 1st law of thermo applies. Two things jumped out - 1. the temperature increase was rapid enough that it reached the saturation within a couple of minutes, and 2. the pressure increase due to thermal expansion represented only a few %. So I am left with the assumption that I have been using - that I am relieving at saturation.

 

[dcasto]

djack, point taken about back to suction vessel would be best. I rarely have suction vessels (1 out of 10 times), so I forget about them.

Solar thermal build up can also be taken careof with a 1/2" check valve around one of the valves that blocks the system in.