Thermal Relief Question 1

[Canoman]

I'm looking at an existing thermal relief valve and trying to calculate a relief load for it. (The client doesn't have this information).

The valve is on the cooling water (tubeside) side of a shell and tube exchanger. The case I'm examining is a blocked exit of the cooling water, while the main process stream is continuing to flow normally.

The process stream is 342°F. The set pressure of the relief valve is 75 psig. So in a blocked exit case, the relieving pressure is 82.5 psig. So if the cooling water gets blocked in, the process will transfer enough heat to vaporize it.

Can anyone offer some advice on how to calculate the relief load for this case? Would the liquid expand enough before vaporization to cause the valve to open, or would it vaporize first?

Thanks, in advance.

 

[25362]

Why should the cooling water vaporize ? Because of liquid thermal expansion, for every one degree Fahrenheit of heating, the pressure would rise by about 55 psi for water at around 90[sup]o[/sup]F.

Whatever the "normal" cooling water "starting" pressure an increase of just a couple of degrees would suffice to activate the thermal relief.

You can estimate the pressure developed on heating "packed-in" liquids by dividing their cubic thermal expansion [α] = 1/V([∂] V/[∂] T)[sub]p[/sub] by their isothermal compressibility [κ] = (1/V)([∂] V/[∂] P)[sub]T[/sub].

Taking the pertinent CRC Handbook data, one sees that for water at 30[sup]o[/sup]C, [α] = 0.000302/[sup]o[/sup]C, and [κ] = 0.0004475/MPa. Their quotient = 0.675 MPa/[sup]o[/sup]C = 54.4 psi/[sup]o[/sup]F.

 

[Canoman]

Weird. I finished my reply, hit preview, and it took me to a page that had only two characters on it. It showed "<." So I'll try my best to recreate my response.

25362,

I think I may not have described the scenario very well. Here's how I'm looking at it. The outlet cooling water line from the exchanger is blocked. Immediately, thermal expansion begins to take place, and liquid begins to relieve. At that point, the pressure in the line is at the relieving pressure. The cooling water supply pressure is significantly lower than the relieving pressure, hence, the cooling water stops flowing. At that point, the heat from the process side goes into the sensible heat duty of raising the cooling water temperature from, say 120°F (cooling water return temperature) to it's saturation temperature @ relieving pressure, of 326°F. Once the volume of liquid cooling water sitting in the exchanger gets to the saturation temperature, the relief valve will have to relieve vapor until the vapor inside the exchanger gets as close to the temperature of the process side as is possible. Once those temperatures are that close, all relief will stop, right? We're still above the cooling water supply pressure so no more will flow in, but we're below the relieving pressure, so nothing will flow out.

Am I missing something? I feel like I'm making this too difficult.

 

[EGT01]

Canoman,

I'm actually more confused by your second post. Based on your description of only one valve blocked (water exit), I would suspect you don't have a thermal relief case if your cooling water supply is a typical distribution header type system. As you noted, water will just expand out through the inlet connection but at a pressure only "slightly greater" than supply pressure and you shouldn't even be close to relief pressure.

Now, if your exchanger is equipped with a "thermal relief valve", I suspect you have an exit and inlet water valve or something else in the inlet that's going to prevent flow out of the exchanger (check valve, control valve) and I really think you should be looking at the situation as if the exchanger water side is liquid full and both exit and inlet are blocked. In other words, there is no other relief path except through your relief system.

Okay, going back to your original question, based on your relief valve set pressure same as your equipment limiting pressure, I think vaporization needs to be considered since your hot side temperature (342F) is greater than the boiling point temperature of your water at maximum pressure allowed for your water side (about 326F at 82.5 psig). API RP-521 has a section titled "3.14 Hydraulic Expansion" that gives some guidance about situations where the blocked in fluid vapor pressure is greater than the relief design pressure and you should review that section. But at 342F, worst case water side vapor pressure is about 107 psig which is questionable as being an acceptable condition even from a hydrotest pressure standpoint on the water side.

For a liquid full system that is blocked in, as the cooling water temperature initially increases, you will need to provide relief for the expanding liquid. When the water temperature reaches the boiling point at relieving pressure, the liquid will begin to vaporize and for a pure component, at constant temperature until all liquid is vaporized. The formation of vapor will require additional considerations.

You should also think about how your relief valve is connected to your system. If it is connected low in your system so it is always below a liquid level, you should check your system to be adequate for not only a liquid expansion rate but also for a liquid rate equal to the rate of vapor generated. In the latter case, vapor can't get to the relief valve until all the liquid is pushed out of the way. Furthermore, in the latter case, you will be relieving a liquid at its bubble point which will likely flash in, and downstream of, your relief valve.

If your relief valve is located at a high point, you "could" take the approach that your relief system needs to be initially adequate for the liquid expansion rate and then eventually for a vapor rate equal to the rate of vapor generated. However, you may not always be willing to accept this approach. Before taking this approach, I would suggest you review the section in API RP-521 "3.15.3 Fluids To Be Relieved". This section actually falls under the "3.15 External Fire" section but I think gives reasonable advice for a liquid full system such as yours.

As far as determining the rate of vaporization, you could use Q = U * A * dT to determine heat input along with the latent heat of the cooling water. I think it would be safe to use the clean, overall heat transfer coefficient from your exchanger design and the exchanger area. Most likely for a blocked in situation on the cooling water side the actual "U" will be less. The temperature difference is the hot side temperature to cold side vaporizing temp.

 

[25362]

I must admit I have assumed the set pressure to be higher than the corresponding boiling point of water. Next time I'll be more careful and better take a look at a steam table.

 

[25362]

Having noted your clarification and EGT01's further excellent explanation, by not having a way to stop back-flow how would you prevent steam from reaching other cooling-water consuming equipment and through it even reaching the cooling tower itself ?

 

[Canoman]

25362 & EGT01,

Thanks for your responses, and that's an excellent point about steam backflow. However, I have been taken off the project, as I had started working on it to help colleagues. Apparently, I didn't have the proper approval. I had approval from my boss, and the person in the other office that I was in contact with, but she didn't have approval to add other people to the project.

I will be sure to bring this up with those who are continuing work on this project.

Thank you very much for your support.