Calculating time to heat a pipe

[MeOHguy]

Dear All,

I am trying to calculate the time to heat a steam pipe from initial operating temperature to an elevated temperature due to failure of a letdown quench station. I have started from the general heat transfer equations (as attached) and I end up with a ridiculously fast time, in less than 1 second.

Then, I came across a closed thread - thread391-318720 and the following equation:

Tg-Tw=(Tg-Twi)e-αt

Using this equation, the time to heat up a pipe is in a matter of minutes. However, I would like to further understand the fundamentals behind this equation.

Could anyone help me?

What goes wrong with my heat transfer equations?

Thanks a lot.

MeOHguy

 

[LittleInch]

I think the issue is one of energy transfer rate.

Your interesting but complex equation wasn't easy to follow and didn't seem to take into account the fact that steam has a relatively low mass compared to the metal. Hence the amount of energy required to heat up the pipe simply isn't there in 1 second. Also the heat transfer rate will be a gradually diminishing one as the pipe heats up. Maybe that's in your equation, but I couldn't follow it.

For a heat up calc without using a transient analysis i would first understand how much energy is available from the steam and how much it takes to heat up the pipe by 10 degrees. Then work in 10 degree steps to gradually reduce the heat transfer rate.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[MeOHguy]

Thanks LittleInch for your feedback.

What is NASA of steam?

Actually, I could only imagine that the moment that the quench water valve fails, the temperature of the steam would increase and there is an increase heat transfer rate, which is covered by the term hi x Ai x (Ti - Tw).

During normal operation, the heat transfer rate is covered by the insulation design, which limits the heat rate to 250 W/m2.

Ya, I tried to derive the equations such that the diminishing heat transfer rate as the pipe is heated up is accounted for. However, the result is just isn't right. When I used the approach that you mentioned, after 10 minutes, the pipe will only be heated by merely 33 K.

 

[LittleInch]

I think you're confusing it all by including the insulation. Forget the insulation layer and just assume that there is no heat transfer from the steel to anywhere else.

Sorry NASA was an error - predictive text on my tablet and I mean mass - I really should read it back before I press submit - I've amended above just so it doesn't confuse anyone else.

By the look of it you have a 16" pipe 23.8mm thick, 30m long. That's 224kg/m or 6.7 tonnes of steel to heat up with a steam supply which I assume whistles through the pipe hence delta T of the steam isn't actually that much?
CP steel of 0.49Kj/kg/K - times mass (6,700kg)
That's 3,280kJ pre degree C.

so 33 degrees takes 108 MJ of energy.

That's a lot of steam (180kW) to heat it up in 10 minutes. Sounds about right to me.



Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[MeOHguy]

I have tried it first with just a bare pipe, but the result was still the same. So, I wonder where I did wrong in solving the integral function.

From the left side of the equation, hi x Ai x (Ti - Tw), when it is computed for a period of 10 minutes, the temperature increase to heat that 7 ton of steel is merely 33K. Obviously, the fundamental equation is correct, I think.

Could anyone help me to check my solution for this integral function? This has been quite mind boggling for the past few days. I regret that I just did not pay 100% attention during the Calculus lessons in the College...

 

[racookpe1978]

you have a dynamic heat transfer problem, but you are starting "too detailed" by beginning with a integral of the various factors that you think describe the problem. Then you are trying to integrate the results over time, but the individual steps are each based on the previous approximations and errors. So it tracks off.

Go back to basics: How much pipe mass has to be heated up by the steam from Temp_0 and time_0? What mass steel, what length, what internal volume of the pipe (max volume of steam if static) and what initial steel temperature? (Assume no losses yet.)

What are the initial steam conditions? Pressure, temp, volume, mass, total energy/enthalpy/entropy? At t=60 seconds, if all that steam condenses, what energy is lost to the steel? Repeat if 90% condenses.
Repeat if 50% condenses. Repeat if only 10% condenses?

Now, back to the dymanic situation: What is the mass flow of the steam? At that speed what is heat transfer coefficients? If that flow is maintained for 15, 30, 60 seconds, how much energy is transferred?