Right now, for example in Tucson, AZ: humidity at 14% with a temperature of 76F and dew point of 24F. High will be 90F :( with Humidity around 6% mid-afternoon.
With 32.2C ambient, 14% RH, 1.35C DWP, the absolute humidity is 4.78 g/m^3
With 24.4C ambient, 14% RH, -4.80C DWP, the absolute humidity is 3.12 g/m^3
This is similar to the AH at BRC. Our current model assumes a DWP of -10C — 10C, so we can predict similar performance. We're not taking into account volumetric capacity and the thermal interface of the heat exchangers. If you know anyone able to help point us in the right direction with those calculations, it would be much appreciated!
Our current understanding is the enthalpy of vaporization + fusion for water is (2257 + 333.55) = 2590.55 J/g we want to pull out of the air. This is assuming we can process enough air, since the dew point is below freezing a fair amount of the time.
This is by using this equation specified in the NASA technical note [0]:
=((0.21668*((TMPC+273)^-1))*((DWPC+273)^-4.9283)*(10^(23.5518+(-2937.4/(DWPC+273)))))*1000
EDIT: Formatting is hard. Added source. Clarification.
A better way to calculate your energy needs would be to look at a steam table, such as the one on Wikipedia's water data page, then take the deltaHvap. This is the accurate enthalpy of vaporization. https://en.wikipedia.org/wiki/Water_%28data_page%29
In theory you need to add the amount of energy to cool the air/vapor mixture to the dew point. However, this amount will likely be small enough to be within your experimental error. For low humidity applications (like Burning Man), you can assume you are cooling mostly air, which is around 1.2 Joules/K per m^3. At 30 K temp differential, and humidity of 4 g/m^3, this is only 9 joules per gram water, or pretty much negligible.
So, you are looking at a deltaHvap of around 2420 to 2450 J/g in this temperature range. This is reasonably close to your original estimate of 2590 J/g, and the good news is that the error is in your favor.
There is always more to read up on and calculate :)
EDIT: The current dehumidifier does accumulate ice on the evaporator coils, depending on the ambient conditions. Once enough ice has accumulated, the compressor turns off and the ice melts into the collection tray. I'm assuming we have to depose the ice out of the dry atmosphere at BRC, since the dew point is below the freezing point of water. Is this not the case?
There are ways to prevent this, although I'm not sure if they would work for your project. Adding salt is a classic, so you can supercool your water while remaining liquid. That's probably not great for drinking water, even with RO. If you can use the melting of the ice as a source of cooling, you can recycle the enthalpy of fusion. It really is a waste and you don't need to pay it. One way to do this is to use the melting ice to lower the heat rejection temperature of your compressor.
However, it may not be worth adding complexity just to cut your energy costs by 15%.
Agreed that it'd be better not to freeze the water at all, but that might be difficult at low dew points.