What is the BTU load for a chiller to maintain a water bath temperature of 34 F?

[DanA2020]

I have been wracking my head about this one... In other jobs I have sized chillers a few times but this one is a bit different.

We have a "Bath" of water, about 400 Gallons
The baths beginning temperature is 34 F
5000 lbs of product runs through this bath every hour at a temp of 40 F
Roughly 220 Gallons of water are lost each hour and replenished by water at 34 F

If there was no chilling system to maintain the water at 34 F then over the course of one hour the water temperature would reach about 38 F

Luckily there are pipes within the bath that flow cold water to maintain a bath temp of 34 F. I need to figure out the BTU load of the chiller needed to supply those cooling pipes to maintain a constant 34 F bath temperature.

Has anyone ever done something like this before? I have tried a few different things to get a rough estimation but my results are all over the place. Any input would be appreciated!

 

[Lnewqban]

Welcome, Dan.
Where those 220 lost gallons/h go to?

 

[DanA2020]

Welcome, Dan.
Where those 220 lost gallons/h go to?

Thanks Lnewqban!

That water attaches to the product flowing through and is lost outside the system during transport or drying (it is recollected for other use but not again in this system)

 

[DaveE]

What is the temperature of the product when it leaves the bath?

 

[DaveE]

Does the chiller also have to chill the replenishment water to 34C? If so what temperature does that water start at?

 

[DaveE]

In your "no chiller" experiment were you replenishing the lost water? If so what was that temperature?

 

[jrmichler]

If I understand correctly:
1) Your makeup water is at the same temperature as the bath (34 F).
2) You are putting 5000 lbs/hr of product at 40 F into the bath.
3) Without the chiller, the bath temperature would rise from 34 F to 38 F in one hour. But you do not say if that temperature rise is from the ambient temperature around the bath, from the product, or both. We need to know that.
4) With the bath at 34 F, what is the temperature of the product leaving the bath?
5) What is the specific heat of the product?
6) Plus the answers to Posts #4, 5, and 6.

 

[DanA2020]

Does the chiller also have to chill the replenishment water to 34C? If so what temperature does that water start at?

-Ideally the Product would leave at 34 F, the product itself is organic and can be calculated as if it were just water.

-The water used to replenish is from a separate already existing chiller

-In the no chiller example I assumed no water loss just to get a baseline

 

[DanA2020]

If I understand correctly:
1) Your makeup water is at the same temperature as the bath (34 F).
2) You are putting 5000 lbs/hr of product at 40 F into the bath.
3) Without the chiller, the bath temperature would rise from 34 F to 38 F in one hour. But you do not say if that temperature rise is from the ambient temperature around the bath, from the product, or both. We need to know that.
4) With the bath at 34 F, what is the temperature of the product leaving the bath?
5) What is the specific heat of the product?
6) Plus the answers to Posts #4, 5, and 6.

Hi jrmichler thanks for the reply, here are the answers:

1) Correct
2)Correct
3) The room is cooled, generally temperatures are between 35-40 F. So Ambient temperature shouldn't have a huge affect
4) Ideally 34 F but the dwell time of the product in the bath is variable from 45-90 seconds
5) Specific Heat is 0.96 btu/lb F

 

[jrmichler]

If we assume:
1) Product enters the bath at 40 F, and leaves at 34 F.
2) Zero heat gain from the room.
3) Zero heat gain from makeup water.

Then the bath chiller calculation is as follows:
5000 lb/hr X 0.96 BTU/(lb F) X (40 - 34) F = 28,800 BTU/hr

Be sure to check the chiller capacity at your operating conditions - 34 F on the cold side, and warmest realistic temperature at the condenser (hot side).