Volume of water removed from sap to arrive at spec percentage of sugar content

[David S]

Hello Members,

I had previously posted this to a thread under Reverse Osmosis because of a similar sap percentage question regarding mixing 2 sap containers with different sugar content. In hindsight, the question is of a different nature and doesn't involve reverse osmosis - just the rendering of a particular mix.

My question relates to the amount of evaporated water, in litres/US gallons/UK gallons, to be removed to arrive at a spec % of sugar content.

The rule of 86 which I have seen reference many places, somehow doesn't seem to work i.e. sap at 2 % therefore:
86 /2 - 1 = 42 US gallons of sap evaporated/removed to achieve 66 % - maple syrup.

For instance: How many litres/US gallons of water are required to be removed from a 100 litres of sap starting at 3 % content to achieve a content of 16 % ? How many litres removed from 100 litres of sap to go from a start of 1.5 % to 10 %?

I realize that there are density changes involved regarding mole(s)/chemistry, but it is probably only fractional for my purposes.

Appreciate any help,

David S

[DrTimPerkins]

First off, to get a better estimate you should be using the revised Jones Rule (http://www.uvm.edu/~pmrc/jones.pdf) and choosing the numerator (the top number) based upon the finished syrup density you desire to achieve.

To use this formula to answer your question, you would first calculate the amount of sap required at each of the densities you are interested in that would be required to make a gallon (or liter) of syrup. Therefore, if we're talking about syrup at 66 Brix (thus we use a numerator of 87.1) for your two examples of 3 and 16 Brix sugar contents it would be.

S = 87.1/3 - 0.32 = 28.71 gallons of sap at 3 Brix
S = 87.1/16 - 0.32 = 5.12 gallons of sap at 16 Brix

By subtraction (28.71 - 5.12) we arrive at 23.6 gal of sap, meaning that you would need to remove 23.6 gal of water from 3 Brix sap to bring it to 16 Brix.

Please understand that these are still just approximations, but are "better" approximations than the original Jones Rule (which was never intended to be used for highly concentrated sap).

[David S]

Hello Dr. Perkins,

Your reply was just what I was looking for - a close/rough estimate. Much obliged.

David

[David S]

Hello Again Dr. Perkins,

Your reply to the reduction of sap was great, however, it did raise some other questions for me.

My original question - How many litres/US gallons of water are required to be removed from a 100 litres of sap starting at 3 Brix content to achieve a content of 16 Brix ?

Your Answer - S = 87.1/3 - 0.32 = 28.71 gallons of sap at 3 Brix
S = 87.1/16 - 0.32 = 5.12 gallons of sap at 16 Brix

By subtraction (28.71 - 5.12) we arrive at 23.6 gal of sap, meaning that you would need to remove 23.6 gal of water from 3 Brix sap to bring it to 16 Brix.

Meaning, correct me if I'm wrong, and sticking with liters, 100 liters at 3 Brix would require approximately 23.6 liters of water removed to arrive at 16 Brix.

How would I calculate say 20,000 Liters at 3 Brix to arrive at 16 Brix - the amount of water to be removed in liters to arrive at 16 Brix ?
I have juggled 20,000 into this equation without success - its probably staring me in the face - old age.

Also, this being a case of reducing to a higher Brix - what about the other way around - say, 1 liter at 66 Brix reconstituted with water to arrive at 16 Brix - the amount of water in liters to be added ?

Appreciate the help.

Regards,

David S

[Super Sapper]

David

In you example you are using 28.71 gallons at 3 brix instead of 100 gallons. You are removing 82.2% of the water in the 3% sap (23.6/28.71) to get to 16%. Multiply 0.822 by the amount of 3% sap to get how many gallons of water need to be removed to get to 16%.

[David S]

Cheers,

Thank you, I thought I was dealing with the 100 gal - instead of using the difference of the two as a %.

David