Fire protection -> heat up time untill critical temperature. 3

[Luuk21]

Hi,

I have the following problem;

We have certain big lines (DN100 till DN250) that are not fire protected (they are insulated but not fire proof). When a fire occurs and the fluid is heated up to 100 degrees Celcius, a chemical reaction could (theoretically) take place. During the fire it is assumed that the electrical installation fails so the line is stagnant.

We want to make sure that the temperature does not reach 100 degrees Celcius within 60 minutes - fire shielding is not possible so we want to apply fire proof insulation. My goal is to calculate the required thickness of the insulation, but I'm unable to find an generally accepted equation for this particular problem.

There are multiple formulas available, I'd like to know if there is a recommended practise/standard.

All relevant properties are known;
Cp, k, rho, epsilon, sigma, etc.

Kind regards,

Luuk

 

[pierreick]

Hi,
Consider this document to support your work.
Pierre

 

[georgeverghese]

Before you get into a knot over these laborious calcs, can you first tell us why you think these pipes may be subject to an external fire ?

 

[Luuk21]

Hi,
Consider this document to support your work.
Pierre

Hi Pierre,
Thanks, but the link doesnt seem to be working at the moment. Could you check on your side or upload it again?
Again, thanks for your help!

Before you get into a knot over these laborious calcs, can you first tell us why you think these pipes may be subject to an external fire ?

Hi George,
Ofcourse. This is the background; it is regarding a plant in India, we have acquired it and we want to bring it to our own company standards of safety.

The concerned lines run (partly) through a building which contain buffertanks of ethanol. Thus a possible fire case. That's basically it.

 

[pierreick]

Hi,
Uploaded .
Pierre

 

[Luuk21]

Hi,
Uploaded .
Pierre

Hi Pierre, it works, thanks! Do you happen to have access to the spreadsheet too?

Cheresources is a website I didn't knew yet, very helpfull, thanks!

Best regards,

Luuk

 

[georgeverghese]

Adding to @pierre's link, to get the inside natural convection htc for stagnant conditions, see page 5-15 in Perry 7th edition, equations 5-39, which indicates Nnu = 3.66 when Ngz=0 at stream velocity=0
This is a long calc since the value for Tb, the fluid bulk temp inside the pipe, varies with time, and so will values for Ts and Tf, the metal surface temp, and the inside film temp. You can break this into 5 time segments ( or 5 values of Tb if you prefer) or more.
Manufacturers for fire proof insulation are easily found on the internet - Chartek is one I am familiar with.

 

[Luuk21]

Adding to @pierre's link, to get the inside natural convection htc for stagnant conditions, see page 5-15 in Perry 7th edition, equations 5-39, which indicates Nnu = 3.66 when Ngz=0 at stream velocity=0
This is a long calc since the value for Tb, the fluid bulk temp inside the pipe, varies with time, and so will values for Ts and Tf, the metal surface temp, and the inside film temp. You can break this into 5 time segments ( or 5 values of Tb if you prefer) or more.
Manufacturers for fire proof insulation are easily found on the internet - Chartek is one I am familiar with.

Hi George,

Thanks for the Perry equation, probably more reliable than my estimation. Calculating the different T's isn't the problem. Finding the thermal resistance for the insulation also not.

The problem I have is finding the right equation. Everywhere I find the equation Q = U * A * dT

Since U is known (all resistances), A is known, (pipe area) and dT is known (Tinside & Tfire), Q can be calculated. This Q is then used to heated up the fluid and you get the new Tinside. It will even specify all the T's at the borders.

Problem is that I think this equation is not correct. First of all, it doesn't take any heat generated by the fire into account. It just assumes the outside temperature (which is still correct). Second - it assumes heat is instantly transported trough the insulation and the wall of the pipe. This is also incorrect.

I can't find the correct expression. I already solved Q = U * A * dT, see excel, but that indicates a required insulation thickness of 3cm, which prevents heating up from 25 to 100 degrees C in 1 hour. Something I cannot believe.

To compare, API-521 recommends Q = C1 * F * A^0.82, which is a factor 100 (!) higher than the heat input calculated by the normal formula. This also gives results I can't use, since if I would substitute this, it assumes a raise of temperature of several degees per second.

 

[georgeverghese]

Is this the right spreadsheet you've loaded up ? It has some jacketed stirred vessel heat transfer calcs, while your first post says it is is for stagnant pipe ?

To me, use a constant external insulation temp of 1100degF to represent the fire. Q will vary depending on the value of Ts and Tf on the inside of the pipe.

By the way, it is very likely the inside surface of the pipe will reach 100degC in a much shorter time than the average bulk temp Tb. So is this acceptable ? If not, then it looks like you have to move these ethanol tanks out of this bldg, or reroute these pipes to avoid an external fire case.

 

[shvet]

@Luuk21
Note that discussion above is useless as math is related to convectional heat exchange only while a firecase is related to radiant and convencional both in some proportion. You are still is in the place where you were atarting this topic.

 

[Luuk21]

Is this the right spreadsheet you've loaded up ? It has some jacketed stirred vessel heat transfer calcs, while your first post says it is is for stagnant pipe ?

Hi George,

Somehow I managed to upload something completely different - indeed, that is not what I wanted to share. See attached file for the right calculation - stagnant pipe with (in this case) water.

By the way, it is very likely the inside surface of the pipe will reach 100degC in a much shorter time than the average bulk temp Tb. So is this acceptable ? If not, then it looks like you have to move these ethanol tanks out of this bldg, or reroute these pipes to avoid an external fire case

Indeed, the temperature I'm searching for is not Ti (Tinside or bulk) but T1, the wall temperature at the pipe. Fortunately this is possible using the (wrong) formula for convection.

@Luuk21
Note that discussion above is useless as math is related to convectional heat exchange only while a firecase is related to radiant and convencional both in some proportion. You are still is in the place where you were atarting this topic.

Exactly, the main question I have is, how do I approach this problem and how do I solve it. I know the normal approach for conduction (which I have used in the Excel sheet).

However, the source of the heat is the problem. I can easily add radiation:

Qnet(t) = sigma * epsilon * Area * (T^4,fire - T^4,inside).

This is the direct heat input from the fire, I have 2 problems with this:

1. No resistance is applied. "So just use the resistance included equation". Will do. As soon as I find the correct one. The only equation I can find is transfer between 2 surfaces. While there is only transfer to 1 surface, then it is further "moved" by conduction.

2. As with the conduction equation, heat is moved "instantly" - the Qin is immediately distributed over the full mass of the pipe.

And this also does not include convection. If I include that as well (which I should) this adds up to another 66 kW of input.

https://engineersedge.com/heat_transfer/convection.htm

(Area = 0.86, Hc = ~100 w/m2*K, very optimistic)

So I'm looking in the wrong places. The conductive equations should work, since the only "heat" that the fluid inside the pipe "feels" is conductive heat. Problem is, how much "heat" to start with, and how to use this in the conductive equation.