Thermal transfer system

[HOTWATER]

I have a hot spring that I want to put a thermal transfer system into for the purpose of keeping a hot tub "hot". The water in the hot spring exits the ground at 7 gallons per minute at 119 degrees F. and is stored in a 5,000 gallon tank that is in the ground. Although there are multiple sources of heat loss, the goal is to try to keep the hot tub at 106 degrees F. I've calculated that I can use 5, 60-foot coils of 1-inch copper tubing, (which is approx. 78 sq. ft of surface area) that would allow a minimum of 50 Gallons of water per minute circulated through it, which is the current flow rate of the existing filter system. If the coil assembly is submerged and the surrounding water in the hot spring reservoir is kept constant at 119 degrees, how many BTU's of heat (per hour) will transfer to the circulating water in the tubing? What is this equivalent to in watts?

Also, what is the BTU rating of 6 GPM of water at 119 degrees?

Thanks to anyone that can help.

 

[poetix99]

There are (at least) two general considerations that govern your geothermal hot tub:

1) a simple energy balance
2) heat exchanger design

I offer a few basic comments at this time:

Energy flows, such as your hot spring, must be based on some reference conditions to define a "zero point". However, the way that energy is (typically) used is to talk about a change of energy. The (arbitrary) reference point then becomes irrelevant when considering the difference of starting and ending energies. This relates to your question about "the BTU rating of 6 gpm of water at 119 degrees"

Your hot spring can be thoutght of providing heat at 119F and giving it to the tub at an average temp. of 106(?). Water's heat capacity is, in round numbers, 1 BTU per pound per Fahrenheit degree. You have 7 gpm = 3500 lb/hr, with 13BTU/lb of "available" heat = 45500 BTU/hr.

You should have an estimate of the heat losses from your tub. Previous posts to this website have discussed losses to ambient from water pools; try a "keyword search" at the top of this page.

If the pool's losses are on the same order of magnitude as the "heat flux" of the hot spring, the design of the heat exchanger becomes more important in actually making this work. If the losses are much smaller - and I have no sense of the numbers in this case - then it probably will not matter very much how you stick the tubing into the geothermal pool.

A comparison of the "available" energy to the energy losses will be one indication of the feasibility of your project. The design the heat exchanger is another.

Your geothermal pool might have thermal stratification, less so if the hot spring flows in from the bottom (rather than being diverted at ground level into a pool). But the assumption of an isothermal pool might not be accurate for the heat exchanger calculations.

Of course, you could skip the design effort, and just hook it up and see...