CO2 injection cooling modeling

[dalcazar]

Hi everyone, it's been a very long time since I had to use my heat transfer knowledge, and the internet is coming up dry with explaining what is involved in the calculation I'm trying to do.

I work for a plant that produces dry food mix that is mostly flour and sugar, and we cool some of our mixes with direct CO2 injection which is delivered to the bottom of the mixer.

My question is: How do you calculate the amount of heat that CO2 needed to cool?
[ul]
[li]The temp of the incoming ingredients and their mass is known.[/li]
[li]The required temp change is known (dT)[/li]
[li]The CO2 comes in as a liquid. I'm assuming that it immediately freezes into dry ice snow?[/li]
[li]How much heat does this expansion/freezing of the CO2 remove from the mix? I'm unable to find a good source for the thermodynamics of this process[/li]
[li]I'm assuming that 246 Btu/lb is the correct heat of sublimation of CO2? (not really trusting the internet for information right now)[/li]
[/ul]

Am I correct to assume that the total CO2 would come from Q[sub]total[/sub]= Q[sub]expansion[/sub] + Q[sub]sublimation[/sub]= m[sub]flour[/sub] * Cp[sub]flour[/sub] * dT

What I'm looking for is the mass of CO2, can anyone clarify the equations and constants involved in the heat from expansion and sublimation that cool the mix so I can calculate the mass therefrom?

Cheers.

Demian

 

[EdStainless]

Unless you are controlling the pressure drop the liquid may be going straight to gas.
The total amount of energy will be the same if the end points are the same.
So Work with heating the liquid, change of state to gas, and heating the gas.

There are some good sites with thermodyamic calculators on them.
Look for ones that site NIST as the data source like carbon-dioxide-properties.com

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube

 

[gruntguru]

So look up the enthalpy of liquid CO2 at the line temp (don't worry about pressure, just assume saturated liquid at the line temp) and the enthalpy of superheated CO2 at the final product temp. The difference is Q[sub]total[/sub]

je suis charlie

 

[georgeverghese]

The superheated CO2 leaving the mixer - cooler may not be at the same temp as the chilled flour - it may be several degC colder - your judgement by how much.

 

[georgeverghese]

Enthalpy values for saturated liquid CO2 and superheated CO2 may be found in Perry's Chem Engg Handbook - chapter on Physical and Chemical properties.

 

[gruntguru]

"The superheated CO2 leaving the mixer - cooler may not be at the same temp as the chilled flour - it may be several degC colder - your judgement by how much."

It could be warmer too. The optimum design would arrange the two streams in counterflow.

je suis charlie

 

[georgeverghese]

Gruntguru,
Agreed, that could be the case also in countercurrent flow. It may be some kind of fluidised bed also.

Dalcazar,
May be this cooler mixer has a temp indicator on exit CO2, so you arent left to guess what this exit gas temp is?

 

[dalcazar]

This is a fluidized bed system, but the mixer is also mecanically turning paddles at all times that the CO2 is being injected so the gas is not the only thing causing mixing. This is not a design application, the mixer as it exists is what I'm stuck with. I'll give the enthalpy of the liquid vs the final superheated gas a shot. I think that will be an acceptable approximation of the heat used.

Thanks everyone.