Is there a calculation to calculate the time/ heat exchange of my wort chiller?

[Elysium]

I am wondering if there is a simple equation that could help me find out how much time I need with my immersion chiller to lower the temp of the wort to pitching temp.

I am wondering if the size of the batch and the temp of the chilling water and the wort would be enough to calculate the time?

Any thoughts on this?

 

[DevilNuts]

I think the length of the copper tube might also play a part.

Way too much math for this guy. I would just boil some water and record how long it takes to cool.

 

[doug293cz]

It's been a while since I studied heat transfer, but solving dynamic cooling (or heating) problems almost always involves differential equations. Now... some folks might consider differential equations "simple" but they're the exceptions.

In addition to the variables you mention, you also need to consider:
1) The flow rate of the cooling water,
2) The geometry of the system (coil diameter & height, pot diameter and wort depth, etc.),
3) Agitation of the coil or circulation of the wort. (If the chiller coil only occupies a small relative volume of the wort, then that volume of the wort will chill quickly, but the wort not near the coil will cool very slowly.)
4) Thermal conductivity & thickness of the coil material, and the heat transfer coefficients of the interfaces between the cooling water and the coil, and the coil and the wort.
5) And, whatever else I have forgotten about.

All that being said, someone may have developed some emperical relationships that might work ok for specific setups. But, the less like the target setup your system is, the worse the emperical equations will work for you.

Easiest thing might be to run some experiments on your system using water in the kettle rather than wort.

Brew on

 

[doug293cz]

Some things you can do to increase the cooling rate with an immersion chiller:
1) Move the coil around in the kettle, or circulate the wort if you have a pump. Cooling is faster the greater the temperature difference between the wort in contact with the coil and the water in the coil. Without agitation, the wort next to the coil cools quickly, and then the cooing rate slows down.
2) If the water exiting the cooling coil is hot, you can get faster cooling by increasing the flow rate, at the expense of more water usage. If the water coming out is cool, then increasing the flow rate won't do much.
3) Put a second coil in an ice water bath, and run the cooling water thru it before the immersion coil. The effectiveness of this will be noticed especially during the later stages of cooling.

Brew on

 

[DevilNuts]

Yes I have noticed that the wort cools faster if you keep it moving around in the kettle. No way how you would work that into a math formula.

 

[freisste]

If you have done it once or twice, the differential equation is actually pretty simple. You would certainly need to assume uniformity based on stirring, cooling water flow, etc and record a data point or two.

That or use a complicated CFD program (computational fluid dynamics), but in my experience, that is much harder due to the garbage in-garbage out effect.

Honestly, I would just try it and see what happens. Then keep that in mind and make simple adjustments based in system changes. If 5 gallons takes 20 minutes, 7 gallons will likely take close to half an hour.

 

[stonebrewer]

The largest factor in cooling is the delta T, or temperature difference. If you are cooling with really cold water, you will bring the temperature down quickly...to a point. As you chill the wort, the delta T becomes smaller and each degree of cooling takes increasingly longer. This is basic thermodynamics. There are definitely formulas and graphs you can find online like this:

Q = mc*Delta T

Q = heat energy ; m = mass, c = specific heat, delta T = the change in temperature

However what you really want is time to cool.

t = 1/K * ln(Ts - Tf/0- Tf).

Problem is K is darn near impossible to define as it depends on too many variables based on your exact setup and geometries and the like. Best thing to do is experiment and try it on your rig. Sorry there isn't a better answer! I suggest measuring the cold water and how long it takes for different temps and graphing it out, then you can interpolate or extrapolate to your hearts content.

Cheers!

 

[BlueHouseBrewhaus]

What were the "What's Your Profession" poll results? I think it was something like 1/3 of us on this site are engineers. I haven't thought about differential equations, thermodynamics or fluid dynamics since I got out of college. It hurts my head! God, I love this site. I think I'll have a beer

 

[freisste]

Engineer. And I overthink things...

 

[theck]

Some things you can do to increase the cooling rate with an immersion chiller:
1) Move the coil around in the kettle, or circulate the wort if you have a pump. Cooling is faster the greater the temperature difference between the wort in contact with the coil and the water in the coil. Without agitation, the wort next to the coil cools quickly, and then the cooing rate slows down.
2) If the water exiting the cooling coil is hot, you can get faster cooling by increasing the flow rate, at the expense of more water usage. If the water coming out is cool, then increasing the flow rate won't do much.
3) Put a second coil in an ice water bath, and run the cooling water thru it before the immersion coil. The effectiveness of this will be noticed especially during the later stages of cooling.

Brew on

+1 Once I put on a second coil in a bucket of ice I went from 25 mins to 15 to cool.

 

[stonebrewer]

I think one mistake people make when cooling, as I did when I first started, is that they have a closed loop for the cooling side...i.e. they are recirculating the cold water, normally to save on water. What I did was add ice over time to get the temp of the cool side back down. It was a lot more work, setup, and things I had to remember to do than I wanted to deal with. So instead, I dump the output into a rain barrel now and use it to water the garden after it cools down. This easily cut 10+ minutes off the process and I didn't have to make and store a lot of ice before each brew day. That said, Doug's suggestion above is a great idea if you want to cut even more time out of your brew day at the expense of a little more setup/prep time. I have an old coil I am not using anymore (switched to a plate chiller), so I might just put that at the front of my cool side, in a bucket of ice water, next brew day just to see what it does for me.

 

[harry_the_face]

1/3 Engineers! I thought there was something wrong with this forum. It reminds me to much of work. I am a non engineer, facility manager for the Corp of Engineers. ;-)

 

[harry_the_face]

I can tell you that it takes me about 20 min to cool to 75 deg with a 1/4 in diameter copper coil 30 ft long in 5gal batch boiled in a keggle. The higher the gravity the beer the longer it will take because the thicker it is.
My coil sits just under the wort so I can't use a 50 ft coil or it will stick out. I also stir the wort constantly while cooling.

 

[freisste]

The higher the gravity the beer the longer it will take because the thicker it is.

Is this true? Water has exceptionally high heat capacity. I thought it went down when adding anything to t (sugar included).

Have you observed this?

 

[doug293cz]

I can tell you that it takes me about 20 min to cool to 75 deg with a 1/4 in diameter copper coil 30 ft long in 5gal batch boiled in a keggle. The higher the gravity the beer the longer it will take because the thicker it is.
My coil sits just under the wort so I can't use a 50 ft coil or it will stick out. I also stir the wort constantly while cooling.

Is this true? Water has exceptionally high heat capacity. I thought it went down when adding anything to t (sugar included).

Have you observed this?

I aggree that wort gravity should not have much effect on the specific heat, since the sp ht of water overwhelms everything else in the system. However, there might be an effect due to the higher viscosity of higher gravity wort, as the higher viscosity will diminish the effectiveness of wort agitation (especially stirring) but not sure if this effect would be easily observable.

Brew on

 

[Yesfan]

+1 Once I put on a second coil in a bucket of ice I went from 25 mins to 15 to cool.

Can you give more details? The temp of your water, how many gallons you were cooling, etc.?


I think my last 5 gallon batch took me 10 minutes to get from boiling to 90F. It was about another 10 to get from 90F to 70F. My immersion chiller is 50ft x 1/2" diameter and my water is around the mid 70s here in SE TN.

I still have my old chiller I bought when I first started (the basic 25ft chiller from Northern Brewer). I've thought about doing the same thing with the bucket technique you did. I think I'll use the faucet until I get down to the 90s, then go the bucket route to bring it down further.

 

[freisste]

However, there might be an effect due to the higher viscosity of higher gravity wort, as the higher viscosity will diminish the effectiveness of wort agitation (especially stirring) but not sure if this effect would be easily observable.

That was all I could think of, but didn't know if I was misunderstanding something else.

 

[balrog]

Sink twice, then third time with ice. Delta T is enough with tap water at first to exchange heat hella-well. When delta T gets small, delta Q (heat excahnge) is lower, hence the ice to increase Delta T.

Having said that, let me say I am still only doing partial boil/partial mash batches but really REALLY like the looks of this thing when I go full boil: WaspWithIceRecircPumpfor$110

 

[Beernik]

A gallon of water weighs 8.34lb.
5 gallons of 1.050 wort should weigh ~43.8lb.
5 gallons of 1.100 wort should weigh ~45.9lb.

So, it will take longer to cool the bigger beer, because you have 2.1lbs more mass to cool in the 1.100 wort.

It's really easy to chill from a boil to 100F because the temperature differential is so great. To get it down from 100F to pitching temperature in a short amount of time requires a prechiller. I have a 25' IC I stick in a bucket with 20lbs of ice as my prechiller.

 

[DevilNuts]

My main challenge is getting below 70F, which seems to be about as cold as my tap is willing to go. I've started keeping about 1/2 gallon of reserve water in the fridge to top off my wort at the end of chilling.

 

[doug293cz]

A gallon of water weighs 8.34lb.
5 gallons of 1.050 wort should weigh ~43.8lb.
5 gallons of 1.100 wort should weigh ~45.9lb.

So, it will take longer to cool the bigger beer, because you have 2.1lbs more mass to cool in the 1.100 wort.

You also need to take into account the fact the specific heat of the wort decreases as the specific gravity increases. Which effect predominates depends on the product of specific heat times specific gravity. If the product of the two is less than 1.0, then wort needs less heat removed in order to cool vs pure water. If the product is greater than 1.0, then wort needs more heat removed.

So, let's look at both effects together. From Pennington and Baker's Sugar: A User's Guide to Sucrose,

S = 1-[0.632-0.001T]*B/100

Where:
S = specific heat
T = temp in deg C
B = degrees Brix​

I was unable to find info on maltose solutions with a quick Google search, so will use info on sucrose, with the assumption that the effects on specific heat are similar enough for our purposes (we already make that assumption for specific gravity.) I took out the sucrose "Purity" term from Pennington and Baker (assume 100% sugar purity) to simplify. The results below show that for all cases of sugar solutions the product of specific gravity and specific heat is less than 1, and that as specific gravity increases, the product decreases. This means that higher gravity worts need less heat removed to cool vs water and lower gravity worts.

I ignored the fact that as the temperature of a specific wort increases, its specific gravity decreases. So my estimates are conservative.

If anyone has information on specific heats of various concentration (specific gravity) worts, we could use that rather than sucrose data to improve the rigor of this analysis.

Please feel free to improve on this analysis.


Brew on

 

[XPLSV]

Just buy a plate chiller...my Therminator drops the temperature of the wort down to 60 F as fast as I can run it through...lower in the winter months.

 

[XPLSV]

Just buy a plate chiller...my Therminator drops the temperature of the wort down to 60 F as fast as I can run it through...lower in the winter months.

Which is, BTW, the Engineering solution, as opposed to the mathematical or physics solution

 

[Beernik]

All solutions are engineering solutions.

 

[XPLSV]

A mathematician, a physicist, and an engineer where standing around at a party, all nervously eyeing a beautiful woman across the room. They discussed their desire to meet this beauty, but all were too shy to approach her. As they discussed possible ways to meet her, a suggestion was put forth that perhaps they needed to approach her in a step by step process…perhaps halving the distance to her, taking a pause, and then doing so again. The conversion quickly turned to whether this would work or not. The mathematician quickly wrote down a series of equations proving that even by halving the distance between them, they would never reach the woman. The physicist also wrote down the same series of equations, but also designed an experiment to prove they would never reach the woman. The engineer glanced at both sheets of paper with the aforementioned writings, drew a couple line strikes through each and declared that he only needed to approach to the point where he would be close enough to reach out and wrap his arms around the beautiful woman.

 

[evanmars]

Or check out this thread for a calculator.

https://www.homebrewtalk.com/f11/immersion-wort-chiller-calculator-376707/#post4720602