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.

Illustration of the ‘heat source paradox’: The lower the performance number (ratio of output and input energy), the lower is the required ambient energy that has to be provided by ‘the environment’. The output heating energy in red is the target number that has to be met – it is tied to the building’s design heat load.

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.

# Things You Find in Your Hydraulic Schematic

Building an ice storage powered heat pump system is a DIY adventure – for a Leonardo da Vinci of plumbing, electrical engineering, carpentry, masonry, and computer technology.

But that holistic approach is already demonstrated clearly in our hydraulic schematics. Actually, here it is even more daring and bold:

There is Plutonium – Pu – everywhere in the heating circuit and the brine circuit …

I can’t tell if this is a hazard or if it boosts energy harvest. But I was not surprised – given that Doc Emmett Brown is our hero:

Maybe we see the impact of contamination already: How should I explain the mutated butterflies with three wings otherwise? After all, they are even tagged with M

Our default backup heating system is … Facebook Messenger!

So the big internet companies are already delivering heating-as-a-service-from-the-cloud!

But what the hell is the tennis ball needed for?

# Cooling Potential

I had an interesting discussion about the cooling potential of our heat pump system – in a climate warmer than ours.

Recently I’ve shown data for the past heating season, including also passive cooling performance:

After the heating season, tank temperature is limited to 10°C as long as possible – the collector is bypassed in the brine circuit (‘switched off’). But with the beginning of May, the tank temperature starts to rise though as the tank is heated by the surrounding ground.

Daily cooling energy hardly exceeds 20kWh, so the average cooling power is always well below 1kW. This is much lower than the design peak cooling load – the power you would need to cool the rooms to 20°C at noon on a hot in summer day (rather ~10kW for our house.)

The blue spikes are single dots for a few days, and they make the curve look more impressive than it really is: We could use about 600kWh of cooling energy – compared to about 15.000kWh for space heating. (Note that I am from Europe – I use decimal commas and thousands dots :-))

There are three ways of ‘harvesting cold’ with this system:

(1) When water in the hygienic storage tank (for domestic hot water) is heated up in summer, the heat pump extracts heat from the underground tank.

Per summer month the heat pump needs about 170kWh of input ambient energy from the cold tank – for producing an output heating energy of about 7kWh per day – 0,3kW on average for two persons, just in line with ‘standards’. This means that nearly all the passive cooling energy we used was ‘produced’ by heating hot water.

You can see the effect on the cooling power available during a hot day here (from this article on passive cooling in the hot summer of 2015)

Blue arrows indicate hot water heating time slots – for half an hour a cooling power of about 4kW was available. But for keeping the room temperature at somewhat bearable levels, it was crucial to cool ‘low-tech style’ – by opening the windows during the night (Vent)

(2) If nights in late spring and early summer are still cool, the underground tank can be cooled via the collector during the night.

In the last season we gained about ~170kWh in total in that way – so only as much as by one month of hot water heating. The effect also depends on control details: If you start cooling early in the season when you ‘actually do not really need it’ you can harvest more cold because of the higher temperature difference between tank and cold air.

(3) You keep the cold or ice you ‘create’ during the heating season.

The set point tank temperature for summer  is a trade-off between saving as much cooling energy as possible and keeping the Coefficient of Performance (COP) reasonably high also in summer – when the heat sink temperature is 50°C because the heat pump only heats hot tap water.

20°C is the maximum heat source temperature allowed by the heat pump vendor. The temperature difference to the set point of 10°C translates to about 300kWh (only) for 25m3 of water. But cold is also transferred to ground and thus the effective store of cold is larger than the tank itself.

What are the options to increase this seasonal storage of cold?

• Turning the collector off earlier. To store as much ice as possible, the collector could even be turned off while still in space heating mode – as we did during the Ice Storage Challenge 2015.
• Active cooling: The store of passive cooling energy is limited – our large tank only contains about 2.000kWh even if frozen completely; If more cooling energy is required, there has to be a cooling backup. Some brine/water heat pumps[#] have a 4-way-valve built into the refrigeration cycle, and the roles of evaporator and condenser can be reversed: The room is cooled and the tank is heated up. In contrast to passive cooling the luke-warm tank and the surrounding ground are useful. The cooling COP would be fantastic because of the low temperature difference between source and sink – it might actually be so high that you need special hydraulic precautions to limit it.

The earlier / the more often the collector is turned off to create ice for passive cooling, the worse the heating COP will be. On the other hand, the more cold you save, the more economic is cooling later:

1. Because the active cooling COP (or EER[*]) will be higher and
2. Because the total cooling COP summed over both cooling phases will be higher as no electrical input energy is needed for passive cooling – only circulation pumps.

([*] The COP is the ratio of output heating energy and electrical energy, and the EER – energy efficiency ratio – is the ratio of output cooling energy and electrical energy. Using kWh as the unit for all energies and assuming condenser and evaporator are completely ‘symmetrical’, the EER or a heat pump used ‘in reverse’ is its heating COP minus 1.)

So there would be four distinct ways / phases of running the system in a season:

1. Standard heating using collector and tank. In a warmer climate, the tank might not even be frozen yet.
2. Making ice: At end of the heating season the collector might be turned off to build up ice for passive cooling. In case of an ’emergency’ / unexpected cold spell of weather, the collector could be turned on intermittently.
3. Passive cooling: After the end of the heating season, the underground tank cools the buffer tank (via its internal heat exchanger spirals that containing cool brine) which in turn cools the heating floor loops turned ‘cooling loops’.
4. When passive cooling power is not sufficient anymore, active cooling could be turned on. The bulk volume of the buffer tank is cooled now directly with the heat pump, and waste heat is deposited in the underground tank and ground. This will also boost the underground heat sink just right to serve as the heat source again in the upcoming heating season.

In both cooling phases the collector could be turned on in colder nights to cool the tank. This will work much better in the active cooling phase – when the tank is likely to be warmer than the air in the night. Actually, night-time cooling might be the main function the collector would have in a warmer climate.

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[#] That seems to be valid mainly/only for domestic brine-water heat pumps from North American or Chinese vendors; they offer the reversing valve as a common option. European vendors rather offer a so called Active Cooling box, which is a cabinet that can be nearly as the heat pump itself. It contains a bunch of valves and heat exchangers that allow for ‘externally’ swapping the connections of condenser and evaporator to heat sink and source respectively.

# Simulating Life-Forms (2): Cooling Energy

I found this comprehensive research report:
Energy Use in the Australian Residential Sector 1986–2020 (June 2008)

There are many interesting results – and the level of detail is impressive: The authors modelled the energy used per appliance type, by e.g. factoring in how building types change slowly over time or by modelling the development of TV sets and their usage. Occupancy factors for buildings are determined from assumptions about typical usage profiles called Stay At Home, At Work or Night Owl.

I zoom in on simulating and predicting usage of air conditioning and thus cooling energy:

They went to great lengths to simulate the behavior of home owners to model operations of air conditioning and thus total cooling energy for a season, for a state or the whole country.

The authors investigated the official simulation software used for rating buildings (from …part2.pdf):

In the AccuRate software, once cooling is invoked the
program continues to assume that the occupant is willing to
tolerate less than optimal comfort conditions and will therefore terminate cooling if in the absence of such cooling the internal temperature would not rise above the summer neutral temperature noted in Table 57, + 2.5oC plus allowances for humidity and air movement as applicable. While this may be appropriate for rating purposes, it is considered to be an unlikely form of behaviour to be adopted by householders in the field and as such this assumption is likely to underestimate the potential space cooling demand. This theory is supported by the survey work undertaken by McGreggor in South Australia.

This confirms what I am saying all the time: The more modern a building is, or generally nowadays given ‘modern’ home owners’ requirements, the more important would it be to actually simulate humans’ behavior, on top of the physics and the control logic.

The research study also points out e.g. that AC usage has been on the rise, because units got affordable, modern houses are built with less focus on shading, and home owners demand higher standards of comfort. Ducted cooling systems that cover the cooling load of the whole house are being implemented, and they replace systems for cooling single zones only. Those ducted systems have a rated output cooling power greater than 10kW – so the authors (and it seems Australian governmental decision makers) are worried about the impact on the stability of the power grid on hot days [*].

Once AC had been turned on for the first time in the hot season, home owners don’t switch it off again when the theoretical ‘neutral’ summer temperature would be reached again, but they keep it on and try to maintain a lower temperature (22-23°C) that is about constant irrespective of temperature outside. So small differences in actual behavior cause huge error bars in total cooling energy for a season:

The impact of this resetting of the cooling thermostat operation was found to be significant. A comparison was undertaken between cooling loads determined using the AccuRate default thermostat settings and the modified settings as described above. A single-storey brick veneer detached dwelling with concrete slab on ground floor and ceiling insulation was used for the comparison. The comparison was undertaken in both the Adelaide and the Darwin climate zones. In Adelaide the modified settings produced an increased annual cooling load 64% higher than that using the AccuRate default settings.

The report also confirms my anecdotal evidence: In winter (colder regions) people heat rooms to higher temperatures than ‘expected’; in summer (warmer regions) people want to cool to a lower temperature:

This is perhaps not surprising, de Dear notes that: “preferred temperature for a particular building did not necessarily coincide with thermal neutrality, and this semantic discrepancy was most evident in HVAC buildings where preference was depressed below neutrality in warm climates and elevated above neutrality in cold climates (ie people preferred to feel cooler than neutral in warm climates, and warmer than neutral in cold climates)” (Richard de Dear et al 1997, P xi).

I noticed that the same people who (over-)heat their rooms to 24°C in winter might want to cool to 20°C in summer. In middle Europe AC in private homes has been uncommon, but I believe it is on the rise, too, also because home owners got accustomed to a certain level of cooling when they work in typical office buildings.

My conclusion is (yet again) that you cannot reliably ‘predict’ cooling energy. It’s already hard to do so for heating energy for low energy houses, but nearly impossible for cooling energy. All you can do – from a practical / system’s design perspective – is to make sure that there is an ‘infinite’ source of cooling energy available.

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[*] Edit: And it actually happenend in February 2017.

Recently I presented the usual update of our system’s and measurement data documentation.The PDF document contains consolidated numbers for each year and month of operations:

Total output heating energy (incl. hot tap water), electrical input energy (incl. brine pump) and its ratio – the performance factor. Seasons always start at Sept.1, except the first season that started at Nov. 2011. For ‘special experiments’ that had an impact on the results see the text and the PDF linked above.

It is finally time to tackle the fundamental questions:

What id the impact of the size of the solar/air collector?

or

What is the typical output power of the collector?

In 2014 the Chief Engineer had rebuilt the collector so that you can toggle between 12m2 instead of 24m

TOP: Full collector – hydraulics as in seasons 2012, 2013. Active again since Sept. 2017. BOTTOM: Half of the collector, used in seasons 201414, 15, and 16.

Do we have data for seasons we can compare in a reasonable way – seasons that (mainly) differ by collector area?

We disregard seasons 2014 and 2016 – we had to get rid of a nearly 100 years old roof truss and only heated the ground floor with the heat pump.

Attic rebuild project – point of maximum destruction – generation of fuel for the wood stove.

Season 2014 was atypical anyway because of the Ice Storage Challenge experiment.

Then seasonal heating energy should be comparable – so we don’t consider the cold seasons 2012 and 2016.

Remaining warm seasons: 2013 – where the full collector was used – and 2015 (half collector). The whole house was heated with the heat pump; heating and energies and ambient energies were similar – and performance factors were basically identical. So we checked the numbers for the ice months Dec/Feb/Jan. Here a difference can be spotted, but it is far less dramatic than expected. For half the collector:

• Collector harvest is about 10% lower
• Performance factor is lower by about 0,2
• Brine inlet temperature for the heat pump is about 1,5K lower

The upper half of the collector is used, as indicated by hoarfrost.

It was counter-intuitive, and I scrutinized Data Kraken to check it for bugs.

But actually we forgot that we had predicted that years ago: Simulations show the trend correctly, and it suffices to do some basic theoretical calculations. You only need to know how to represent a heat exchanger’s power in two different ways:

Power is either determined by the temperature of the fluid when it enters and exits the exchanger tubes …

[1]   T_brine_outlet – T_brine_inlet * flow_rate * specific_heat

… but power can also be calculated from the heat energy flow from brine to air – over the surface area of the tubes:

[2]   delta_T_brine_air * Exchange_area * some_coefficient

Delta T is an average over the whole exchanger length (actually a logarithmic average but using an arithmetic average is good enough for typical parameters). Some_coefficient is a parameter that characterized heat transfer for area or per length of a tube, so Exchange_area * Some_coefficient could also be called the total heat transfer coefficient.

If several heat exchangers are connected in series their powers are not independent as they share common temperatures of the fluid at the intersection points:

The brine circuit connecting heat pump, collector and the underground water/ice storage tank. The three ‘interesting’ temperatures before/after the heat pump, collector and tank can be calculated from the current power of the heat pump, ambient air temperature, and tank temperature.

When the heat pump is off in ‘collector regeneration mode’ the collector and the heat exchanger in the tank necessarily transfer heat at the same power  per equation [1] – as one’s brine inlet temperature is the other one’s outlet temperature, the flow rate is the same, and also specific heat (whose temperature dependence can be ignored).

But powers can also be expressed by [2]: Each exchanger has a different area, a different heat transfer coefficient, and different mean temperature difference to the ambient medium.

So there are three equations…

• Power for each exchanger as defined by [1]
• 2 equations of type [2], one with specific parameters for collector and air, the other for the heat exchanger in the tank.

… and from those the three unknowns can be calculated: Brine inlet temperatures, brine outlet temperature, and harvesting power. All is simple and linear, it is not a big surprise that collector harvesting power is proportional temperature difference between air and tank. The warmer the air, the more you harvest.

The combination of coefficient factors is the ratio of the product of total coefficients and their sum, like: $\frac{f_1 * f_2}{f_1 + f_2}$ – the inverse of the sum of inverses.

This formula shows what one might you have guessed intuitively: If one of the factors is much bigger than the other – if one of the heat exchangers is already much ‘better’ than the others, then it does not help to make the better one even better. In the denominator, the smaller number in the sum can be neglected before and after optimization, the superior properties always cancel out, and the ‘bad’ component fully determines performance. (If one of the ‘factors’ is zero, total power is zero.) Examples for ‘bad’ exchangers: If the heat exchanger tubes in the tank are much too short or if a flat plat collector is used instead of an unglazed collector.

On the other hand, if you make a formerly ‘worse’ exchanger much better, the ratio will change significantly. If both exchangers have properties of the same order of magnitude – which is what we deign our systems for – optimizing one will change things for the better, but never linearly, as effects always cancel out to some extent (You increase numbers in both parts if the fraction).

So there is no ‘rated performance’ in kW or kW per area you could attach to a collector. Its effective performance also depends on the properties of the heat exchanger in the tank.

But there is a subtle consequence to consider: The smaller collector can deliver the same energy and thus ‘has’ twice the power per area. However, air temperature is given, and [2] must hold: In order to achieve this, the delta T between brine and air necessarily has to increase. So brine will be a bit colder and thus the heat pump’s Coefficient of Performance will be a bit lower. Over a full season including the warm periods of heating hot water only the effect is less pronounced – but we see a more significant change in performance data and brine inlet temperature for the ice months in the respective seasons.

# Data for the Heat Pump System: Heating Season 2016-2017

I update the documentation of measurement data [PDF] about twice a year. This post is to provide a quick overview for the past season.

The PDF also contains the technical configuration and sizing data. Based on typical questions from an ‘international audience’ I add a summary here plus some ‘cultural’ context:

Building: The house is a renovated, nearly 100-year old building in Eastern Austria: a typical so-called ‘Streckhof’ – an elongated, former small farmhouse. Some details are mentioned here. Heating energy for space heating of two storeys (185m2) and hot water is about 17.000-20.000kWh per year. The roof / attic had been rebuilt in 2008, and the facade was thermally insulated. However, the major part of the house is without an underground level, so most energy is lost via ground. Heating only the ground floor (75m2) with the heat pump reduces heating energy only by 1/3.

Climate: This is the sunniest region of Austria – the lowlands of the Pannonian Plain bordering Hungary. We have Pannonian ‘continental’ climate with low precipitation. Normally, monthly average temperatures in winter are only slightly below 0°C in January, and weeks of ‘ice days’ in a row are very rare.

Heat energy distribution and storage (in the house): The renovated first floor has floor loops while at the ground floor mainly radiators are used. Wall heating has been installed in one room so far. A buffer tank is used for the heating water as this is a simple ‘on-off’ heat pump always operating at about its rated power. Domestic hot water is heated indirectly using a hygienic storage tank.

Heating system. An off-the-shelf, simple brine-water heat pump uses a combination of an unglazed solar-air collector and an underwater water tank as a heat source. Energy is mainly harvested from rather cold air via convection.

Addressing often asked questions: Off-the-shelf =  Same type of heat pump as used with geothermal systems. Simple: Not-smart, not trying to be the universal energy management system, as the smartness in our own control unit and logic for managing the heat source(s). Brine: A mixture of glycol and water (similar to the fluid used with flat solar thermal collectors) = antifreeze as the temperature of brine is below 0°C in winter. The tank is not a seasonal energy storage but a buffer for days or weeks. In this post hydraulics is described in detail, and typical operating conditions throughout a year. Both tank and collector are needed: The tank provides a buffer of latent energy during ‘ice periods’ and it allows to harvest more energy from air, but the collector actually provides for about 75% of the total ambient energy the heat pump needs in a season.

Tank and collector are rather generously sized in relation to the heating demands: about 25m3 volume of water (total volume +10% freezing reserve) and 24m2 collector area.

The overall history of data documented in the PDF also reflects ongoing changes and some experiments, like heating the first floor with a wood stove, toggling the effective area of the collector used between 50% and 100%, or switching off the collector to simulate a harsher winter.

Data for the past season

Finally we could create a giant ice cube naturally. 14m3 of ice had been created in the coldest January since 30 years. The monthly average temperature was -3,6°C, 3 degrees below the long-term average.

(Re the oscillations of the ice volume are see here and here.)

We heated only the ground floor in this season and needed 16.600 kWh (incl. hot water) – about the same heating energy as in the previous season. On the other hand, we also used only half of the collector – 12m2. The heating water inlet temperatures for radiators was even 37°C in January.

For the first time the monthly performance factor was well below 4. The performance factor is the ratio of output heating energy and input electrical energy for heat pump and brine pump. In middle Europe we measure both energies in kWh 😉 The overall seasonal performance factor was 4,3.

The monthly performance factor is a bit lower again in summer, when only hot water is heated (and thus the heat pump’s COP is lower because of the higher target temperature).

Per day we needed about 100kWh of heating energy in January, while the collector could not harvest that much:

In contrast to the season of the Ice Storage Challenge, also the month before the ‘challenge’ (Dec. 2016) was not too collector-friendly. But when the ice melted again, we saw the usual large energy harvests. Overall, the collector could contribute not the full ‘typical’ 75% of ambient energy this season.

(Definitions, sign conventions explained here.)

But there was one positive record, too. In a hot summer of 2017 we consumed the highest cooling energy so far – about 600kWh. The floor loops are used for passive cooling; the heating buffer tank is used to transfer heat from the floor loops to the cold underground tank. In ‘colder’ summer nights the collector is in turn used to cool the tank, and every time hot tap water is heated up the tank is cooled, too.

Of course the available cooling power is just a small fraction of what an AC system for the theoretical cooling load would provide for. However, this moderate cooling is just what – for me – makes the difference between unbearable and OK on really hot days with more than 35°C peak ambient temperature.

# Tinkering, Science, and (Not) Sharing It

I stumbled upon this research paper called PVC polyhedra:

We describe how to construct a dodecahedron, tetrahedron, cube, and octahedron out of pvc pipes using standard fittings.

In particular, if we take a connector that takes three pipes each at 120 degree angles from the others (this is called a “true wye”) and we take elbows of the appropriate angle, we can make the edges come together below the center at exactly the correct angles.

A pivotal moment: What you consider tinkering is actually research-paper-worthy science. Here are some images from the Chief Engineer’s workbench.

The supporting construction of our heat exchangers are built from standard parts connected at various angles:

The final result can be a cuboid for holding meandering tubes:

… or cascaded prisms with n-gon basis – for holding spirals of flexible tubes:

The implementation of this design is documented here (a German post whose charm would be lost in translation unless I wanted to create Internet Poetry).

But I also started up my time machine – in order to find traces of my polyhedra research in the early 1980s. From photos and drawings of the three-dimensional crystals in mineralogy books I figured out how to draw two-dimensional maps of maximally connected surface areas. I cut out the map, and glued together the remaining free edges. Today I would be made redundant by Origami AI.

I filled several shelves with polyhedra of increasing number of faces, starting with a tetrahedron and culminating with this rhombicosidodecahedron. If I recall correctly, I cheated a bit with this one and created some of the pyramids as completely separate items.

I think this was a rather standard hobby for the typical nerdy child, among things like growing crystals from solutions of toxic chemicals, building a makeshift rotatable telescope tripod from scraps, or verifying the laws of optics using prisms and lenses from ancient dismantled devices.

The actually interesting thing is that this photo is the only trace of any of these hobbies. In many years after creating this stuff – and destroying it again – I never thought about documenting it. Until today. It seems we weren’t into sharing these days.