Exit Temperature from hot drainage system

[Im Nari]

Hi All. I've been lurking on this site for quite a while and I've learned a ton. I've come across a problem, though, that I'm having a lot of trouble with. I'm not sure that I'm approaching it in a valid way, and I figured I should reach out to those possibly in the know to see if I'm overlooking a simpler approach.

I'm currently designing a drainage system which will, upon emergency shutdown of equipment in an industrial facility, receive hot condensate and drain it to a lift station, where it will then be pumped elsewhere. I'm interested in the inlet temperature of the fluid into the wet well of the lift station, as it will inform me if I will have adequate NPSHa for the pumps or if I need to implement other precautions during drainage events. I've been scouring the web attempting to find resources outlining how to calculate this exit temperature and I've found the following, which seem the most relevant to this situation:

Heat Transfer In Buried Liquid Pipelines
Heat Transfer Model of Above and Underground Insulated Piping Systems

Additionally I have read chapter 14 of Transport Phenomena from Bird, Stewart, and Lightfoot in an attempt to understand this further. The issue I'm running up against is this: all of these sources are concerning the fluid's temperature distribution in laminar and turbulent pipe flow, while I'm dealing with channel flow in a partially filled pipe. Does anyone know of a method I can use for achieving what is outlined in the above sources for channel flow in an underground drainage line?

I thought there might be some way to approximate the channel flow as some equivalent pipe flow, for which I can just use the above techniques, but I don't know where I'd begin with that, or if that is even a valid approach to begin with.

Any insight would be much appreciated!

Thanks,
Nari

 

[1503-44]

If your pipe is buried, I don't think you said, and not very long, it will not experience significant cooling. I'll guess-timate 1°C/km
or less. If its above ground, it depends more on the coldest night temp and wind. But in both cases, heat loss through the pipe wall is by conduction, so it's highly dependent on wetted surface area.

A partially full pipe will not have the full diameter contact to allow maximum heat transfer by conduction through the full pipe wall, only through the wetted surface. For a decent approximation to a full flow method, simply assume the heat transfer will be reduced by the same amount of reduced contact area you have, i.e. your heat transfer will be wetted circumference / full circumference x heat transfer of a full pipe.

A black swan to a turkey is a white swan to the butcher ... and to Boeing.

 

[Im Nari]

Yes, it's buried. Sorry I forgot to specify that.

I guess I don't completely understand the ratio method you outlined. Doesn't the mass difference between the two situations play a factor? A half full pipe of nominal diameter x will have the same surface area to liquid mass ratio as a full pipe of nominal diameter x over the same pipe length, right? Plus it will additionally lose some heat to the air in the pipe. Maybe I'm misunderstanding something; I don't have a very strong background in heat transfer.

Regardless, I've been coming to the same conclusion as you on the temperature loss. It seems like it won't lose enough heat in time and I'll have to implement some drainage tempering measures. I guess I'm just a little frustrated that I can't find a way to calculate this. Just to know, ya know?

The other additional element to this situation is that it's a transient process as opposed to the steady state processes which are outlined in those references I've found. Those pipes are going to be sitting cold and empty most of the time until an emergency drainage event occurs.

 

[1503-44]

The hot air is still inside the pipe, so yes that too will also be conducted from air to pipe wall, but relatively little heat is contained by the air, as its mass is very small in relation to the mass of the water. Water density is 62.4 pcf, air at atm pressure is 0.07 pcf. I would ignore the air. If you chose to include it, or if you consider that the portion of the heated pipe contacted by the water conducts that heat to all its circumference, both assumptions will bring you closer to a full pipe flow solution.

If you are looking for the coolest exit temperature, use partial pipe contact. If you are looking for the highest exit temperature, assume a full pipe.

There are many example calculations of calculating heat loss by an insulated pipe on the Internet. Probably even some online calculators. I believe there will be little difference if the pipe is full or not. The only difference you have is that instead of an industrial insulation, you may have a few feet of soil acting as the insulation. Dry soil is actually a pretty good insulator. You can search for references of heat conductivity values for various soil types.

A transient situation helps reduce the water exit temperature some, because some heat will be lost in heating up the soil around the pipe, but that is a temporary process. Once the soil is warmed up and in thermal equilibrium, you are back to the typical "steady state heat loss through an insulated pipe" problem again. A steady state full pipe flow solution will give you the highest possible exit temperature.

Your link explains the calculations. Maybe some online calculators here.

https://duckduckgo.com/?q=heat+loss+insulated+pipe+calculator&t=brave&ia=web

Unless your pipe is a few kilometers long, or your soil is at-20°C or something, I would assume that there is no temperature reduction.

A black swan to a turkey is a white swan to the butcher ... and to Boeing.

 

[Im Nari]

That makes sense and is convincing to me. Thanks for your help!

 

[pierreick]

Hi,
Yes the outlet temperature will be # same than the inlet temperature ,let say Tin - 0.5 C .Share data about your system ( fluid , pipe size, flow rate, Temp fluid in , Temp soil ,fluid properties (cp, Ro, viscosity ), pipe material , insulation material , conductibility pipe, conductibility insulation, bury depth ) to get numbers
Good luck
Pierre