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The maximum reachable efficiency for a heat pump can be calculated using Lorenz/Carnot cycle:

$COP = \frac{T_H}{T_H - T_C}$

Where as the $T_H$ is the target temperature and $T_C$ is the reservoir temperature (I might be wrong about the exact terminology).

In case of heating houses with brine-water the temperature of brine can exceed 50°C where as the target temperature is max 25°C.

  1. How does the formula translate for this scenario, is it even considered heating?
  2. If its not considered heating, would it be logical to step up the brine temperature and store the energy in containers for house use?
  3. What is the typical method of incorporating heat pumps with high temperature brine-water sources?
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    $\begingroup$ 50 degree C brine would be geothermal heating. You don't need a heat pump to move heat from cold to hot, just a heat exchanger $\endgroup$
    – Tiger Guy
    Commented Jan 15 at 13:59
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    $\begingroup$ @TigerGuy "Move heat from cold to hot" needs work... Moving heat from Hot to Cold does not. $\endgroup$
    – Solar Mike
    Commented Jan 15 at 14:12
  • $\begingroup$ @SolarMike, yes, I got it backwards $\endgroup$
    – Tiger Guy
    Commented Jan 15 at 19:19
  • $\begingroup$ @TigerGuy considering we want to achieve certain Co2/kWh of output heat, (Co2 for electricity generation), how would this formula change? is it a better way to calcualte Heatpump efficiency using thermodynamics ? $\endgroup$
    – Ali
    Commented Jan 16 at 9:00
  • $\begingroup$ Is the heat to be transferred direct from the hot brine to the indoor air, or is there a secondary water loop/system involved? In the former case, @TigerGuy's comment applies, but you have to worry about how you're going to get hot tap water hot enough for all the hygiene purposes one wants hot tap water to serve. In the latter case, a heat pump might indeed be useful. $\endgroup$ Commented Jan 16 at 13:54

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Heat pump efficiency is the heat output over the power input. For heat pumps and refrigeration systems, this efficiency is a positive number because you can move more heat than the energy you put in. So COP is used because calling a system 300% efficient just raises more questions.

Since heat pumps are made to move heat from cold to hot (from outside at 5C to inside at 22C), the equations fall down if you are trying to use one to move heat from hot to cold (outside at 50 to inside at 22). People don't build complicated systems to move heat from hot to cold because heat flows this way naturally. All it takes is a heat exchanger. In this case, you would use your 50 degree ground temp water and blow air over a coil with that 50 degree water in it. My guess is that you would be less efficient than this by doing it with a system that evaporates and condenses fluids. You would only need to pay to pump the water and blow the air.

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