Calculating needed cooling power

I am currently doing a project(it is a part of my education) on a cooling unit for a chemical company. They have removed a big load an old screw compressor and it is currently running on a 7%-17% load:/ That is not good..

I am doing some calculations on some possible options to replace this old screw compressor.

The screw compressor is in 10 out of the 12 months supplying some chemical reactors and it is possible to determine the cooling capacity by measurement. But two months a year they are using the unit to a special production where methanol is to be cooled down to -10°C.

It has to be cooled from 40°C to -10°C in 210 min. So I am able to calculate an average cooling power to approximately 32 kW.

I have also been able to calculate the possible heat transfer through the heat exchanger when temperature differens between cooling liquid and the methanol are at its highest there will be no problem in transfering 32 kW. But when I reach -5°C on the methanol I am not able to transfer more than 24kW.

So my question is. In a mathematical manner. How would you do calculations in this case? I do know that if I install a unit that can deliver more than 32 kW I can transfer more heat in the first period so that i do not have to transfer 32kW through the hole process.

But how could I prove this in a mathematical way?

I hope I have made myself understandable, as I find it hard to express myself in english when it become technical. Feel free to ask if there are something that I haven't made clear.

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have also been able to calculate the
possible heat transfer through the heat exchanger when
temperature differens between cooling liquid and the
methanol are at its highest there will be no problem in
transfering 32 kW. But when I reach -5°C on the methanol
I am not able to transfer more than 24kW.

Why can't you transfer as much heat at -5 compared to +40??

Methanol has more heat energy per Kg at -5 than +40?
So if the heat is there why can't it be transferred?

What refrigerant is your primary?

Regards
Rob

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Oh by the way

Welcome to the site

:)

Rob
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Thank you.

It is a 30% CaCl2 solution running in a cooling jacket on a reactor in which the methanol is located. Is it the cooling jacket which is not able to transfer the heat.
It is calculated with the formula P=U×A×deltaT. So when delta to between brine and methanol becomes smaller as the methanol cools down. It won't be able to transfer as much heat.