Calculating if sea water will freeze in exposed pipe 3

[doug223]

Hi Everyone
I am trying to calculate if (at all) sea water will freeze inside a pressurised 12" carbon steel pipeline at 5 bar. The water will be non moving so I assume mass flow rate will be 0?

The wind speed will be taken to be 12.5 m/s. Air temp has been -15 C last night.

I have been following this guide attached. I have found in my search that the specific heat of sea water (generally) is 3985 J kg K.

I have found info for fresh water but not finding it as straightforward for a saltwater application.

Any help is greatly appreciated.

 

[doug223]

Attached guide is below.

 

[ione]

Seawater freezing point is related to its salinity (salt presence lowers freezing point). You can assume on the average -2 °C (28.4 °F) to be the freezing point.

The following approach can give you an idea of time required to turn seawater into ice.

You have a non-flowing mass M of seawater. Knowing the pipe diameter and its length you can calculate it.

Consider the energy required to turn water into ice has two contributions:

1. That due to sensible heat: Q1 = M*cp*deltaT
Being
cp the specific heat [kJ/(kg*°C)]
deltaT temperature difference from water starting temperature and freezing poit.
2. that due to latent heat of solidification: Q2 = M*L
Being
L the latent heat of solidification (approx 335 kJ/kg)


Assume your pipe is at seawater starting temperature.
Evaluate air properties at film temperature Tf = (Tamb + Twall)/2.

You can then use the following calculator (convection calculator/forced/across circular road) to get your heat transfer coefficient htc [W/m^2/°C]

http://www.thermal-wizard.com/tmwiz/default.htm

Then you can calculate time t required to turn seawater into water solving the equation below

htc*A*deltaT =(Q1 + Q2)/t

where A is the outer surface [m^2] of your pipe.

 

[Dave41A]

doug:

I agree with everything ione has posted except for the last equation. This assumes a linear cooling rate.

Rather, the cooling will be exponential (e^-t/tau) while the water is still liquid, and then essentially constant* while the water is freezing. The time constant for the system ("tau") is simply m*c/(h*A), where m is the mass of the system, c is the specific heat, h is the htc, and A is the external surface area. Your "m" and "c" should be "lumped," that is, computed to reflect the mass and specific heat of the steel in the pipe and the water inside it. The water will probably dominate since its "c" is so high compared to steel. While the water is liquid, this is a classic first order differential equation "Newton's law of cooling" problem. Once freezing begins, the heat rate will be constant (Q=htc*A*Delta T), with the freezing rate of the salt water being determined by its specific heat of solidification.

For your design concerns, since it seems that the pipe is pressed full (no air), your concern may actually be the onset of freezing. If the pipe is closed at both ends, even the slightest bit of freezing will raise the pressure in the pipe considerably (due to the expansion of the water as it freezes). In other words, the pipe does not need to freeze solid to burst. If you have pressure relief, you may be able to ignore this, assuming it works under freezing conditions.

Good luck,

Dave

*splitting hairs, the fresh water actually freezes out of the salt water, creating fresh ice and brine. The freezing point of the remaining brine is lower than that of the original salt water mixture, so the heat rate is not exactly constant during freezing. Add to this that some salt does get entrained in the otherwise fresh ice, changing the behavior of the mixture further. If the ice forms on the perimeter of the pipe, (freezing from outside in) the ice itself will have an insulative effect, slowing the freezing rate even more. A conservative approximation is to ignore this.

 

[IRstuff]

Is this for school?

TTFN

FAQ731-376
Chinese prisoner wins Nobel Peace Prize

 

[MintJulep]

Amazing what you can find in the internet.

http://www.csgnetwork.com/h2ofreezecalc.html

 

[zdas04]

Dave41A,
Good explanation. I have a question about the last statement in the "splitting hairs" section. When you say

If the ice forms on the perimeter of the pipe, (freezing from outside in) the ice itself will have an insulative effect, slowing the freezing rate even more. A conservative approximation is to ignore this.

Why would ignoring that phenomena be more conservative? If you define "conservative" in this case as "determine the minimum time to bulk phase change and its coincident volume change" then I agree. But if you define it as "the predicted time to the absence of liquid" then ignoring the insulation effect would be optimistic.

David

 

[ione]

I am not that sure the lumped capacitance approach is applicable for the bulk of seawater.
The first step to validate such a model, is a preliminary analysis of the Biot number. If Bi<0.1, then a lumped model will lead to a small error (not higher than 5%). Whilst for the metallic pipe wall the lumped model could lead to acceptable results, the quite low thermal conductivity of water and the characteristic length involved make me a bit sceptical (just an opinion).

 

[Compositepro]

Salt water freezing in a pipe is different from open water,in that the salt will concentrate in the unfrozen water and lower the freezing point. This makes it much more difficult to freeze completely solid.

 

[doug223]

Hi Again

The application is a pipeline in a fire pump system. Just trying to work out if it will freeze as if it is possible then we would have to trace heat and/or lag the piping.

Ione, I followed your approach but ended up with 2.4 micro seconds! Can I ask why on the thermal wizard site I would be using forced convection over a rod? Would it be a tube instead? I know that the water would not be flowing inside but they will have different values?

I will try the expontential cooling rate and see what happens.

Thanks guys

 

[ione]

The approach which foresees the Newton’s cooling law and so an exponential temperature decay (as suggested by Dave41A) is undoubtedly more correct than the one I’ve proposed, and it better depicts what really happens. Anyway I still have doubts concerning the use of a lumped capacitance model to describe seawater behaviour inside the pipe. The “lumped” approach leads to acceptable results when conduction heat transfer mechanism dominates and by far over convective heat transfer mechanism. The parameter to say when “by far” is enough is the Biot number, and the condition to be verified is Bi<0.1. The lumped capacitance model could be particularly reliable when dealing with metals (high thermal conductivity) having a little characteristic dimension and when dealing with natural convection.

And now to your question concerning the Thermal wizard. I suggested the circular rod bar model as this is the geometry closer to that of a tube amongst those available in Thermal wizard. Standing to what above is allowable to consider the pipe wall being all at the same temperature and, at the beginning of the cooling process, to assume the pipe surface is at the same temperature as that of seawater. Dealing with forced convection you’ll have a very high heat transfer coefficient, which will decrease as the temperature lowers, and this further complicates your problem.

 

[doug223]

Thanks for going through it ione much appreciated

I guess what I am trying to do is work out if sea water at 4.5 deg C can be cooled to -2.33 deg C inside the pipe. This temperature will induce the onset of freezing. The water will flow at worst case once a month so its quite a long time for it to sit there. I think as what was already mentioned there could be some phase change at the pipe surface but stop not far after as the salinity will increase.
I do have some small heat transfer experience but mainly calculating heat sink size.

Thanks Again

 

[Dave41A]

zdas04: To answer your question on the "conservative approximation," your first reading is the way that I meant it. If the insulative effect of the ice is considered, the rate of freezing will slow. If this was for an icemaker, then you are right--ignoring the ice formation would be optimistic.

ione: Good point on the Biot number, but as you observe, typically the Biot is used for solid materials. If one makes the (reasonable?) assumption that the water keeps itself "well mixed," (uniform temperature) with natural convection, then the lumped capacitance model applies. Verifying this for this case would be an elaborate exercise. However, I do not think that is needed here because the latent heat of freezing of water is so high and any ice that forms will be in direct contact with liquid water. Because of this, I would be surprised if any appreciable thermal gradient developed within the water within the pipe, but for the record this is entirely my guess, not proof.

doug: external convection coefficients (from the pipe to the air) depend soley on the external geometry of the system. The air acts on the outer surface of the pipe and the internal configuration is irrelevant. Hence, the external convection coefficient for a tube is the same as for a rod.

That said, if this pipe is really going to sit unused for a month at a time in -15C weather, I strongly suggest draining the pipe and putting it in standby in a dry state. If it's a firemain, it needs to be ready to go when needed. A couple quick-acting drain valves could probably be installed with a minimum of cost. Heating/lagging are other options, as you describe.

Since the pipe is pressed full (no air) just a partial freeze will be enough to rupture the pipe, leaving you without fire protection. Years ago, I spent some time in polar regions and we kept our external fire stations drained for this reason.

Good luck,

Dave

 

[vpl]

A star for you Dave. Sometimes practicality needs to be considered.

Patricia Lougheed

******

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[ione]

Doug,

In the light of your last post I’m 100% with Dave14A. The pipe is likely to burst before seawater got completely frozen
(take a look at this thread

http://www.eng-tips.com/viewthread.cfm?qid=287419&page=3)

The onset of ice with its 9% volume growth would cause many bother. Draining the pipe is IMO the cheapest option available.

 

[racookpe1978]

From a reliability standpoint, I'd much rather trust a drained and dry pipe rapidly filling with "unfrozen" water to a static pipe that I "hope" was always correctly and permanently and always heated by a generator and wires that themselves needed to be always running under Arctic conditions.

An empty pipe will be known to get pressurized in 2-6 seconds. A broken and frozen pipe will be thought safe and reliable until it is needed immediately. Then Murphy will tell you if the freeze protection worked.

 

[KiwiMace]

The summary of that calc attached above seemed clear to me - eventually it will freeze. If they can't be dry, bury them deep, run them through heated spaces, or trace and lag them.

For the dry pipe idea - Not all pipes are 2-1/2" diameter. I doubt you are going to find too many practical solutions to filling a half mile of 12" pipe in the code allowed 60 seconds.