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# Flare radiant heat transfer on atmospheric tank - heat transfer calc

## Flare radiant heat transfer on atmospheric tank - heat transfer calc

(OP)
I am installing a flare fairly close to an atmospheric tank, and am trying to determine the minimum height of the flare. I have generated isopleths for the governing cases, which give thermal radiation flux values (btu/hr sq ft). I wish to estimate the amount of vaporization of liquid in the tank. It would seem that using the flux rate solely might be too conservative, as this does not take into account the resistance to heat transfer through the insulation, tank wall, and inside coefficient.

Anyone have an opinion on this? If you agree, then do you have a suggestion for how to convert the flux value into a resistance term?

### RE: Flare radiant heat transfer on atmospheric tank - heat transfer calc

You can set up the software to plot temperature curves (isotherms) around the flare for each scenario and see what is the maximum radiated temperature at the tank top surface. This is the maximum (theoretical) temperature tank contents can see, if exposed to radiation long enough. Some software tools have ability to plot these temperature curves vs. time, and by taking into account wind (chill) effects. In reality, the maximum fluid temperature inside the tank will still be lower than the maximum radiation temperature, due to heat dissipation and thermal resistance to heat transfer. Not sure what is the exact background of the problem and why you need this calculations and how accurate they need to be, but the approach I just described will probably have sufficient accuracy to cover 99% of all possible cases/reasons.

If you need more rigorous results, some advanced modeling tools will be required.

Dejan IVANOVIC
Process Engineer, MSChE

### RE: Flare radiant heat transfer on atmospheric tank - heat transfer calc

One shouldn't assume that the heat flux into an insulated tank is equal to the radiant heat intensity generated by the flare. The amount of radiant heat that ends up passes into the tank contents is only a fraction of the radiant heat that strikes the insulated tank. Much of that radiant heat energy is reflected by the metal insulation cover. The heat that gets into the tank contents is conducted from the hot insulation cover, through the insulation to the tank wall, and then from the tank wall to the tank contents. That's a fairly easy composite wall heat transfer calculation. You'll need to determine the emissivity of the insulation cover, the thermal conductivity of the insulation material, and an estimated film coefficient for heat transfer from the wall to the tank contents (I assume that's vapor since the tank isn't operated full of liquid). Even if you assume a generous film coefficient, you'll find that most of the radiant heat doesn't make it into the tank.

### RE: Flare radiant heat transfer on atmospheric tank - heat transfer calc

(OP)
Thanks for the responses. Don, actually I am trying to take the approach that you laid out. My confusion is converting the flux term (btu / hr sq ft) to a heat transfer coefficient, which I then could use in combination with the remaining resistences.

For example, I know that a certain point on the tank that the flux from the flame center is 200 btu/hr sq ft. I believe I can come up with an absorptivity coefficient (probably .25), but I can't think of how to integrate this with the remaining resistantcies to heat transfer. I suppose if I could estimate the temperature of the flame that might help.

Thanks again for the help.

### RE: Flare radiant heat transfer on atmospheric tank - heat transfer calc

A film coefficient doesn't apply for radiation. Film coefficients apply when heat is transferred by conduction from a moving fluid stream. What you have is radiation that's directly striking the insulation cover, causing it to heat up. In order to calculation the heat that's transferred through the subsequent resistances you start with a temperature of that metal cover. As radiation pores heat into the cover, its temp will rise until it either melts (if it's aluminum) or until it reaches an equilibrium temperature, at which point the heat radiated into the cover equals the heat lost from the cover (through radiation and conduction) to the atm.

### RE: Flare radiant heat transfer on atmospheric tank - heat transfer calc

The 200btu/hr/ft2 arriving at the tank insulation comprises of the following subsequent modes of heat transfer, which depends strongly on the surface temp of aluminum jacket
a) Heat absorbed which depends on the absorption coeff of the surface
b) Heat reradiated which depends on the emissivity of the surface
c) Heat dissipated by natural convection along the outside vertical surface of the aluminum jacket, and we could assume no wind cross currents

Each of these terms can be computed if we know what Ts is.

Further, component (a) must also travel across the insulation layer, the tank wall (assume zero resistance) and the not insignificant internal natural convection htc/ resistance, assuming there are are no forced internal convection currents.

Start with some trials on Ts, compute (a), then compute (b) and (c) and see if the total sums up to 200btu/hr/ft2 of external surface. For initial trials, we could assume the internal nat convection htc inside the tank to be negligible.

### RE: Flare radiant heat transfer on atmospheric tank - heat transfer calc

(OP)
I wanted to follow up on this. I have incorporated several of the ideas suggested into my calcs. Due to the heat flux on the roof of the vessel, the amount of energy imparted to the vapor space will be significant. Any ideas on calculating a heat transfer coefficient between the boiling material in the tank and the vapor. This tank contains ammonia at saturation (very low temperature - the vapor temp will be much higher). Vaporized ammonia is removed via a compressor. We are trying to estimate the amount vaporized to see if the compressor can handle.

Normal convention would be to disregard any heat transferred to the dry walls of the tank (roof and top of side walls), but since the btu/hour in the roof is 10-15 higher than on the wetted walls, I thought I should consider the affect of the roof flux.

Should I consider a htc on from the vapor to liquid? If so, any recommendations on a method to calculate the htc?

Bill

### RE: Flare radiant heat transfer on atmospheric tank - heat transfer calc

The vapor layer at tank top would add a significant resistance layer to heat transfer from the roof wall down to the liquid for convection mode - so would suggest this may be ignored in comparison to radiation mode heat transfer.

Radiation component may be significant, since the liquid ammonia would be at -35degC or so , and will depend on inside roof wall temp. Radiation view factors (F) for this mode are in Perry Chem Engg Handbook in the chapter on Radiation Heat Transfer - I used the graph for view factors between parallel planes / discs on a similar calc some years ago. Also include emissivity values for the 2 surfaces as required.

Startup tank cooldown vaporisation rates would usually be the controlling case for boil off gas compressor duty estimates, but agree in this case, these external heat leaks into the tank may be large also. Also account for heat leak from the soil into tank bottom, and any other tank surfaces that may be deliberateley left uninsulated.

### RE: Flare radiant heat transfer on atmospheric tank - heat transfer calc

The equations and figures relevant to deriving the radiant heat trasferred between the inside roof wall and the boiling liquid, with reference to Perry Chem Engg Handbook 6th edn., are figure 10-48 and equations 10-195 and 10-200. Obviously, the roof inside surface temp used in this derivation must match that obtained from the same quantity of heat transferred through the resistances making up the roof wall facing the atmosphere (ie external insulation, ignoring resistance at roof wall ).

### RE: Flare radiant heat transfer on atmospheric tank - heat transfer calc

Presume you're aware that solar radiation should be added to this flare radiation only component of 200btu/hr/ft2 incident on these tank walls to get total incident radiation. Solar radiation ranges 200-300btu/hr/ft2 depending on geographic location.

### RE: Flare radiant heat transfer on atmospheric tank - heat transfer calc

(OP)
George,
Thanks for the input. I had not thought of the radiation inside the tank (from tank walls to liquid surface). I have several old copies of Perry's, plus the 8th edition. Trying to come up with 6th edition to be sure I am looking at the equations/figure you referenced. Thanks,
Bill

### RE: Flare radiant heat transfer on atmospheric tank - heat transfer calc

In case you see the 7th edition, see figure 5-15, equations 5-125, 5-132. I dont have editions earlier than the 6th. The view factor figure is an abstract from "Radiant Heat Transfer" by Hottel and Sarofim.

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