Prandtl number of a g/l mixture (Ethane at phase transition)

[Juvenalis]

I have a problem in finding the heat transfer coefficient of a heat exchanger in which Ethane undergoes a phase transition. I would like to find the Prandtl number of Ethane in the phase transition region. So far I thought I would use the following:

Pr_av = x * Pr_g + (1-x) Pr_l

Pr_av = The Prandtl number of the mixture
Pr_g = The Prandtl number of the vapor (found in table)
Pr_l = The Prandtl number of the liquid (found in table)
x = the vapor quality of the mixture

However, I do not know whether this is correct. Should I calculate the Prandtl number from the (average Specific heat * average dynamic viscosity)/(average thermal conductivity)

If so, how do I calculate these properties for my g/l mixture? Right now I don't even know how to calculate the specific heat at the boiling point.

 

[Chestermiller]

I have a problem in finding the heat transfer coefficient of a heat exchanger in which Ethane undergoes a phase transition. I would like to find the Prandtl number of Ethane in the phase transition region. So far I thought I would use the following:

Pr_av = x * Pr_g + (1-x) Pr_l

Pr_av = The Prandtl number of the mixture
Pr_g = The Prandtl number of the vapor (found in table)
Pr_l = The Prandtl number of the liquid (found in table)
x = the vapor quality of the mixture

However, I do not know whether this is correct. Should I calculate the Prandtl number from the (average Specific heat * average dynamic viscosity)/(average thermal conductivity)

If so, how do I calculate these properties for my g/l mixture? Right now I don't even know how to calculate the specific heat at the boiling point.

This is not how I would approach this.
Tell us a little more about this heat exchanger, please.

Condenser or evaporator?
Temperature and pressure?
Inlet conditions and outlet conditions?
What is the fluid or gas on the other side of the tube wall?
Flow rates?
Number of shell passes and tube passes.

Do you expect a large pressure drop?

Chet

 

[Juvenalis]

Hi Chet, I'm just trying to make a preliminary calculation on a LNG gasification heat exchanger. I tried to find a numerical solution for my problem but I am interested in finding the local heat transfer coefficient in the region where Ethane undergoes a g -> l phase change.

Im calculating for the simple case of a parallel plate heat exchanger (counterflow)

Cold side:
LNG (95% Methane, 5% Ethane)
Inlet: -146.5 Celsius 200 bar
Outlet: -131 Celsius 200 bar
Flowrate: 1kg/s

Hot side:
Ethane
Inlet: -65.73 Celsius, 3 bar, vapor quality 0.46
Outlet: -65.73 Celsius, 3 bar, vapor quality 0.16
Mass flow: 0.3 kg/s

Pressure drop will be low.

I am just interested in finding the local heat transfer coefficient and thought to do this with the Dittus Boelter correlation (Nu = 0.023 * Re^0.8 * Pr ^0.33)which I washoping to find a way to calculate the Prandtl number for condensing Ethane.

 

[Juvenalis]

Is it a problem to calculate a heat transfer coefficient, or the prandtl number, or the specific heat of a fluid during phase change? Any of those would answer my question.

 

[Chestermiller]

OK. I get the picture. You have a pure condensing vapor on one side and a non-condensing gas on the other side. The resistance on the non-condensing gas side is going to dominate. According to BSL, the heat transfer coefficient on the non-condensing gas side is typically going to be in the range 2-20 Btu/hr-ft^2-F, and the heat transfer coefficient on the condensing vapor side is typically going to be on the order of 200-2000 Btu/hr-ft^2-F. First determine the heat transfer coefficient on the Me/Et side to ascertain that it is in this range. This should give you some comfort in neglecting the heat transfer resistance on the condensing vapor side, and save you some time. If you're still not comfortable enough with this, assume a worst case of 200 on the Et side, so that you're conservative.

I can see what you are trying to do, but you ought to ask yourself if it's really worth it to get the extra degree of refinement you are seeking. Doing two phase flow is difficult. In your system, you're going to have a thin layer of liquid covering the wall, and this is going to be the main resistance. The problem is, you don't know how thick that layer of liquid is going to be. The temperature gradient is going to be within the liquid layer.

Hope this helps a little.

Chet

 

[Juvenalis]

Hi Chet, I get the idea: If the heat transfer coefficient is much higher on one side than on the other I can neglect its contribution to the thermal resistance.

However, The Methane/Ethane side is not a non-condensing gas, it's a cryogenic liquid. Will the heat transfer coefficient of the condensing vapor still be much larger than the heat transfer coefficient of the cryogenic liquid.

 

[Chestermiller]

Hi Chet, I get the idea: If the heat transfer coefficient is much higher on one side than on the other I can neglect its contribution to the thermal resistance.

However, The Methane/Ethane side is not a non-condensing gas, it's a cryogenic liquid. Will the heat transfer coefficient of the condensing vapor still be much larger than the heat transfer coefficient of the cryogenic liquid.

Probably. Just calculate it and see what you get.