Heat Pumps: Coefficient Of Performance

The COP of a heat pump is a function of the temperatures where heat is delivered and withdrawn:

COP formula

Formula 1: Coefficient of performance of heatpumps. η is the efficiency of the motor/compressor and is normally 0.4 .. 0.6, Thigh is the temperature at which the heat is delivered, Tlow the temperature at which the heat is withdrawn. All temperatures in K.

In England and Holland for example, the average temperature is 17.3°C inside and 4.8°C outside during the heating season. When ΔTcon = ΔTevap = ΔT = 20°C and η= 0.5, COP = 3.0 When ΔT = 5°C, COP = 6.6. With a fine wire heat exchanger, ΔT could be as low as 3°C, which gives a COP of 8.

This means we can heat a home with a heatpump using outside air as a heat source. We use the following configuration:

heat pump system with fiwihex fans and tubehex heat exchangers

Figure 1: Heating a home with a heatpump, using outside air as a heat source. High-efficiency heat exchangers are used to keep temperature differences to a minimum.

We use three 200 W/K Fiwihex fans outside (600 W/K total) and seven 100 W/K Fiwihex fans inside (700 W/K total)and two 1000 W/K tubehex propane to water heat exchangers. Our home is 130 W/K and the mean temperatures are 4.8°C outside and 17.3C inside. The temperature difference is 12.5C, so we need to pump 1625W to keep the house warm. This will cause a Tlow of 4.8 -(1625/600) - (1625/1000) = 0.5°C. Inside, Thigh will become: 17.3 + (1625/700) + (1625/1000) = 21.2C. When we substitute this in formula 1, we get a COP of 7.1.

The three 200 W/K fans outside could be Ø90 cm and spin @ 73 RPM. They would use 46W of electricty with a motor efficiency of 50%. Inside they could be Ø40 cm and 233 RPM and use 20W. With two 15W pumps and a compressor that uses 1625/7.1=229W, the total power is 325W. This gives a "real" COP, including all secondary systemsof 5.0.

When we use ground water, or a ground-coupled loop, we can pump from 10C. We don't need any Fiwihex fans outside and Tlow becomes: 10 - (1625/1000) = 8.4C, Thigh (using the same seven fans) stays 21.2C. This gives a "raw" COP of 11.4 and a "real" COP of 8.5!

These COP values are not just optimistic calculations: we reached 90% of theroretical COP values with a crude heatpump from standard HVAC parts, with propane (R290) as refridgerant. The COP will further increase when high efficiency scroll compressors and DC brushless fan motors are used.

A great advantage of these high efficient heat-exchangers is that all circuit temperatures are below 40°C with no pressure at all, so the water circuits can be made from cheap plastic tubes. This allows the consumer to install his own heatpump or airconditioning, because there are no copper refridgerant tubes anymore, just water pipes.

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