Compressing air with a paddlewheel on a river

I ran across a website which includes a long video and several short videos of a paddlewheel which can compress air using river water flow and a spiral pump. They go to a lot of trouble to get rotary motion from their compressed air, but there are other uses.

One use for low pressure compressed air might be to pump heat out of the "cold" reservoir.

And one way to pump heat (I'm not sure if it is a good way) is using a bubble pump. Actually, I'm not even sure it is pumping heat. What is happening is heat already in the gas is being converted to work, lowering the temperature of the gas, and heat from the water is flowing into the gas, which does more work and absorbs more heat. Then the gas is released into the ambient at the water temperature. If the air started at the water temperature, then the internal energy of the air has not changed. All of the heat removed from the water was stored as gravitational potential energy of pumped water.

The compressed air would be stored up and used during the coldest time of day. First it is chilled via heat pipes carrying heat to a radiator cooled by the ambient temperature. We certainly don't want to warm the water with hot compressed air just before cooling it! The idea is to do some work using the cold air to produce water colder than ambient.

Next, the cold air is used in a bubble pump to raise cold water, cooling the water further. Finally, the cold water is used to cool the top of heat pipes carrying heat out of the cold reservoir.

So, how much heat is removed from the water by expanding air? Would it be better to use some heat from the hot reservoir to heat the air and use work extracted from the hot air to operate a conventional refrigerant-mediated heat pump? Would it be better to simply operate the main heat engine at night, using the heat from the hot reservoir and dumping waste heat directly to the ambient?

The amount of heat removed is the difference in work done by adiabatic expansion vs. isothermal expansion of the gas.  That difference depends on the heat capacity of the gas.  A gas with low heat capacity cools more when it does a given amount of work.  …

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