How Much Is Enough?

The other day I got to wondering if I could improve Eolian's freezer - to make it colder, or to make the cold last longer, by fine-tuning the amount of propylene glycol in the holding plates.

But first, a word of explanation.  Eolian has two separate compartments for the refrigerator (one holding plate) and the freezer (two holding plates), but both are cooled by a single compressor.  The refrigerator has a thermostat in it, which closes a valve in the refrigerant line when the setpoint is reached.  The freezer on the other hand has no valve, and continues to chill - until the compressor shuts itself off.

So I decided to do put my education to work and do a little Chemical Engineering.

You may remember that in a previous post I discussed the phase diagram for the propylene glycol-water system earlier.  I suggest you go back and read that one now, because I will proceed presuming you have...

But this diagram unfortunately does not have any actual temperatures or concentrations delineated on it.  So I prepared an expanded version of the portion to the left of the eutectic point from some published data:

Portion of Propylene Glycol-Water Phase Diagram

But even this covers too much territory.  What we are interested in is just this portion:

The Part We Care About

As I mentioned in that previous post, I spoke at length with a Technautics sales rep at a Seattle boat show, and he recommended a 15% solution for freezer holding plates.  I don't know what the concentration in ours is (that is something I should rectify...), but let's assume that 15%.  Here it is plotted on the diagram:

 

The vertical pink line describes a 15% concentration.  Let's follow what happens as the temperature is dropped, moving down the pink line at the 15% concentration.  At first, the liquid just gets colder.  But at a temperature of 22°F we meet the line.  At this point, the first freezing occurs.  And what freezes out is ice - pure water ice.  Because of this, the amount of water remaining in the liquid phase is reduced, increasing the concentration of propylene glycol. 

Now let's look at the situation at 15% glycol cooled to 10°F... the intersection of the two pink lines.  By this point, we have frozen out a substantial amount of ice, removing water from the liquid phase.  In fact, the concentration of glycol in the liquid phase has followed the black curve down, and is now about 27% (the concentration of the total mixture has not changed - it is still 15%).  And the Lever Rule tells us that the total mixture is a slush of 12/27 = 44% ice and 15/27 = 56% glycol solution.

Now why did I draw the horizontal pink line at 10°F?  Because that is the lowest temperature our compressor can reach with our current refrigerant.    A low pressure switch cuts it off.  The only way to decrease this endpoint would be to change out the pressure switch (not recommended - the manufacturer decided that this is the lowest pressure at which the compressor should operate), or to change to a refrigerant that has a higher vapor pressure.  In fact, we have already done that; we replaced the original R-12 with R-409a, which indeed has a higher vapor pressure.  So 10°F is as cold as it can get in our freezer.

So that's one point settled:  The low temperature is 10°F.  Now how to maximize the time that the holding plates can maintain the cold?

 It is important to keep in mind that the holding plate is going to operate over a range of temperatures.  In our current case, once the compressor shuts off, the first bit of ice begins to melt, at a temperature of 10°F, diluting the glycol solution.  As more ice melts, the temperature rises, until finally when the last bit melts, the temperature of the mixture has reached 22°F.

To then summarize, with a 15% solution, the holding plates will operate over a temperature range of 10°F -> 22°F, and have a cooling capacity representing 44% of the total original solution.

We could increase the amount of glycol in the plates... say to 20%.  The plates would then operate over a temperature range of 10°F -> 18°F, and have a capacity representing only 26% of the total original solution (calculation left as an exercise for the reader).  So we would give up nearly half of our capacity to maintain temperature in exchange for a 4°F drop.  Doesn't seem like a fair trade.

OK, how about if we go the other way?  What happens if we decrease the glycol concentration?  Let's try 10%, the concentration that the Technautics rep recommended for refrigerator holding plates.  Now the holding plates operate over a range of 10°F -> 26°F, with a capacity representing 63% of the original solution.  Wow!  We increased our capacity by 50%!  But we have to tolerate an upper temperature of 26°F.  I think that is uncomfortably warm for a "freezer"...  many foods will not be solid at this temperature because their water content is saturated with eg. sugar - like ice cream.

Conclusions

• Technautics has it right.  The 15% concentration provides a good balance between capacity and temperature range.
• And I need to assess the glycol concentration in our freezer holding plates.

* Someone is almost certain to suggest that the glycol concentration be raised to 30%, or even more, to get a lower freezing point.  That would certainly accomplish that, but because of the limitations of the compressor and refrigerant, we would never reach that freezing point.  In fact, the holding plates would have zero capacity the way it was assessed above - they would contain nothing but liquid at the compressor cutoff, and would begin warming immediately.  The magic of the holding plate is the ice - melting a gram of ice at 32°F to a gram of water at 32°F absorbs 80 times more heat than raising the temperature of that same gram of water from 32°F to 33°F. 

How Much Is Enough?