I'm starting a project to build a heatpump. It's a simple device from many prospectives, but finding some of the math critical to designing a refrigeration system can be hard to find. What I'm building is a water-source heatpump, a device which uses electricity to pump heat from one water source to another. This works very much like the air conditioning you might have at your house. In fact, most of the parts are from an air condition unit that was damaged and scrapped.

The design of water-source heatpump goes something like this. There are two heat exchangers, one for the water to be chilled and another for the water that will be heated (some systems are reversible, so the heat source/destination can be switched; my system will not incorporate a reversing valve). Those heat exchangers put the refrigerant very close to the water, with only a thin layer of metal separating them. Between the loops are a compressor and a metering device, arranged so the compressor liquefies the refrigerant, the superheated refrigerant goes through one of the heat exchanger, to the metering device where it is expanded to a supercooled gas, then through the other heat exchanger, and back to the compressor.

My design uses loops of pipe for the heat exchangers. A small copper pipe is fed through a larger PEX pipe, the inner copper pipe will hold the refrigerant while the outer PEX pipe holds the water. This can be done with two copper pipes, one inside the other, but the PEX should be cheaper and provide a bit of insulation compared to using an outer copper pipe. The other common heat exchanger is a plate heat exchanger. plate exchangers are much more compact, and highly effective with large temperature differentials. My design calls for a very low temperature differential, hence the loop design.

When designing the loop heat exchangers you need to know how long the loops need to be made. I'm familiar with commercially available heat exchangers of a similar design, so I know roughly how large the piping needs to be, and roughly how long. But I wanted to know with better precision than that, and getting a straight answer out of an engineer can be a task. After much mulling about I've come to these design guides (which are based on experiments conducted at the University of Perdue, where the estimated error was <13%):
3/8" ARC Type-A in 3/4" PEX - 26 ft.°F/Ton 1/2" ARC Type-A in 1" PEX - 19 ft.°F/Ton The above are for R-410a (Puron), the most common refrigerant in modern residential air condition equipment. For R-22 (Freon) multiply by 1.2, this also applies to R-22 equipment running R-290 (Propane). So what do those numbers actually mean? I'm running my liquid line in 3/8" ACR(A) within a 3/4" PEX pipe; I need a loop 26 feet long to be able to deliver 1 Ton of cooling at 1°F temperature differential (or exchange loss). If I want 2 Tons of cooling, I can just double the 26 feet to 52 feet. 1°F differential is extremely little, which is why you'd never see a 26 foot loop in a 1 Ton commercial unit. A differential less than 5°F is doing pretty good, and 10°F might still be acceptable for some projects. I'm aiming for 4°F, with a 1.7 Ton compressor (capable of 2.25 Tons under select conditions), so loops about 12 feet long. I'll actually be using longer loops (about 16 feet) as I plan to build three of these units, and a ARC tubing commonly comes in 50 foot coils.