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.
elkemental Force 
You don’t happen to know where I could find the advertisement, do you? I do have one friend that will get a good belly laugh.
There was only a non-English version of that ad :-)
Agreed, very misleading. As a side note, I find it very common that supposed experts on refrigeration so often disparage heat input absorption cycles over their lower apparent COPs. The authors often fail to calculate the electrical generation efficiencies, losses transmission and so on, in their calculations of vapor compression COP. There are certainly practical issues regarding the implementation of absorption, but the comparisons are typically misleading, unless marketers get involved…Ha – then you get clever statements like you shared here.
I know so few people that would appreciate this.
Totally agree – such comparisons are often misleading if ‘systems boundaries’ are not clearly defined. I think here we have are at least three different official ways of calculating seasonal performance factors (… w/o brine circulation pumps, w/o heat distribution circuits and buffer tank losses …) and there can be spectacularly high so-called ‘COPs’ via including a solar thermal system that just heats the same hot water buffer tank as the heat pump – but is otherwise not combined with the heat pump directly.
Losses in generation and distribution of electrical energy are at least accounted for in our energy certificates for new homes now – so people see e.g. that their heat pump’s performance factor needs to be at least 3 if their electrical power comes mainly from thermal power plants. It’s hardly ‘green’ to run a gas turbine that generates 40% electrical power, compared to simply burning that gas ‘de-centralized’ at nearly 100% efficiency at home.
I laughed a bit at the end. That advertisement is exactly the kind of thing I would have been asked to write after some sort of ‘sales and creative’ team brainstorming session in marketing. It always terrified me that I’d encounter something I couldn’t sufficiently research, and become one of those contributing to such misleading statements.
I remember how it feels to reply to requests of proposals (on behalf of my employer, as the ‘technical expert’): In this case you know exactly what technical downsides ‘your’ product have, but it is a game-like challenge to answer the questions in a way that is true but still does not fully reveal the shortcomings. Like: Does your product support standard X? You would not say No (which was true) but rather: It supports standard Y that is related to X because blah blah …