It is not a paradox – it is a straight-forward relation between a heat pump system’s key data:
The lower a heat pump’s performance factor is, the smaller the source can be built.
I would not write this post, hadn’t I found a version of this statement with a positive twist used in an advert!
In this post I consider a heat pump a blackbox that converts input energy into output heat energy – it ‘multiplies’ energy by a performance factor. A traditional mechanical heat pump uses electrical input energy to drive a mechanical compressor. The uncommon Rotation Heat Pump utilizes the pressure gradient created by centrifugal forces and thus again by electrical power.
But a pressure difference can also be maintained by adsorption/desorption processes or by changing the amount of one fluid dissolved in another; Einstein’s famous refrigerator uses a more complex combination of such dissolution/evaporation processes. Evaporation or desorption can be directly driven by heat: A gas heat pump thus ‘multiplies’ the energy from burning natural gas (and in addition, a heat pump and a gas boiler can be combined in one unit).
The overall performance factor of a gas heat pump – kWh heating energy out over kWh gas in – is about 1,5 – 2. This is lower than 4 – 5 available with mechanical compressors. But the assessment depends on the costs of kWh gas versus kWh electrical energy: If gas is four times cheaper (which nearly is the case in Germany) than burning natural gas in a traditional boiler without any ‘heat pump multiplication’, then the classical boiler can be more economical than using a heat pump with an electrical compressor. If gas is ‘only’ two times as cheap, then a gas heat pump with an overall performance number of ‘only’ 2 will still beat an electrical heat pump with a performance factor of 4.
While the gas heat pump may have its merits under certain market conditions, its performance number is low: For one kWh of gas you only get two kWh of heating energy. This means you only need to provide one kWh of ‘ambient’ energy from your source – geothermal, water, or air. If the performance factor of an electrical heat pump is 4, you multiply each kWh of input energy by 4. But the heat source has to be able to supply the required 3 kWh. This is the whole ‘paradox’: The better the heat pump’s performance is in terms of heating energy over input energy, the more energy has to be released by a properly designed heat source, like ground loops sufficiently large, a ground-water well providing sufficient flow-rate, an air heat pump’s ventilator powerful enough, or our combination of a big enough solar/air collector plus water tank.
If you wish to state it that way, a heat pump with inferior performance characteristics has the ‘advantage’ that the source can be smaller – less pipes to be buried in the ground or a smaller water tank. And in an advert for a gas heat pump I found it spelled out exactly in this way, as a pro argument compared to other heat pumps:
The heat source can be built much smaller – investment costs are lower!
It is not wrong, but it is highly misleading. It is like saying that heating electrically with a resistive heating element – and thus a performance number of 1 – is superior because you do not need to invest in building any source of ambient energy at all.