Can the Efficiency Be Greater Than One?

This is one of the perennial top search terms for this blog.

Anticlimactic answer: Yes, because input and output are determined also by economics, not only by physics.

Often readers search for the efficiency of a refrigerator. Its efficiency, the ratio of output and input energies, is greater than 1 because the ambient energy is free. System’s operators are interested in the money they pay the utility, in relation to the resulting energy for cooling.

If you use the same thermodynamic machine either as a refrigerator or as a heat pump, efficiencies differ: The same input energy drives the compressor, but the relevant output energy is either the energy released to the ‘hot side’ at the condenser or the energy used for evaporating the refrigerant at the ‘cool side’:

The same machine / cycle is used as a heat pump for heating (left) or a refrigerator or AC for cooling (right). (This should just highlight the principles and does not include any hydraulic details, losses etc. related to detailed differences between refrigerators / ACs and heat pumps.)

For photovoltaic panels the definition has sort of the opposite bias: The sun does not send a bill – as PV installers say in their company’s slogan – but the free solar ambient energy is considered, and thus their efficiency is ‘only’ ~20%.

Half of our generator, now operational for three years: 10 panels, oriented south-east, 265W each, efficiency 16%. (The other 8 panels are oriented south-west).

When systems are combined, you can invent all kinds of efficiencies, depending on system boundaries. If PV panels are ‘included’ in a heat pump system (calculation-wise) the nominal electrical input energy becomes lower. If solar thermal collectors are added to any heating system, the electrical or fossil fuel input decreases.

Output energy may refer to energy measured directly at the outlet of the heat pump or boiler. But it might also mean the energy delivered to the heating circuits – after the thermal losses of a buffer tank have been accounted for. But not 100% of these losses are really lost, if the buffer tank is located in the house.

I’ve seen many different definitions in regulations and related software tools, and you find articles about how to game interpret these guidelines to your advantage. Tools and standards also make arbitrary assumptions about storage tank losses, hysteresis parameter and the like – factors that might be critical for efficiency.

Then there are scaling effects: When the design heat loads of two houses differ by a factor of 2, and the smaller house would use a scaled down heat pump (hypothetically providing 50% output power at the same efficiency), the smaller system’s efficiency is likely to be a bit lower. Auxiliary consumers of electricity – like heating circuit pumps or control systems – will not be perfectly scalable. But the smaller the required output energy is, the better it can be aligned with solar energy usage and storage by a ‘smart’ system – and this might outweigh the additional energy needed for ‘smartness’. Perhaps intermittent negative market prices of electricity could be leveraged.

Definitions of efficiency are also culture-specific, tailored to an academic discipline or industry sector. There are different but remotely related concepts of rating how useful a source of energy is: Gibbs Free Energy is the maximum work a system can deliver, given that pressure and temperature do not change during the process considered – for example in a chemical reaction. On the other hand, Exergy is the useful ‘available’ energy ‘contained’ in a (part of a) system: Sources of energy and heat are rated; e.g. heat energy is only mechanically useful up to the maximum efficiency of an ideal Carnot process. Thus exergy depends on the temperature of the environment where waste heat ends up. The exergy efficiency of a Carnot process is 1, as waste heat is already factored in. On the other hand, the fuel used to drive the process may or may not be included and it may or may not be considered pure exergy – if it is, energy and exergy efficiency would be the same again. If heat energy flows from the hot to the cold part of a system in a heat exchanger, no energy is lost – but exergy is.

You could also extend the system’s boundary spatially and on the time axis: Include investment costs or the cost of harm done to the environment. Consider the primary fuel / energy / exergy to ‘generate’ electricity: If a thermal power plant has 40% efficiency then the heat pump’s efficiency needs to be at least 2,5 to ‘compensate’ for that.

In summary, ‘efficiency’ is the ratio of an output and an input energy, and the definitions may be rather arbitrary as and these energies are determined by a ‘sampling’  time, system boundaries, and additional ‘ratings’.

The Collector Size Paradox

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 is the impact of the size of the solar/air collector?


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.

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.

Heat Transport: What I Wrote So Far.

Don’t worry, The Subversive Elkement will publish the usual silly summer posting soon! Now am just tying up loose ends.

In the next months I will keep writing about heat transport: Detailed simulations versus maverick’s rules of thumb, numerical solutions versus insights from the few things you can solve analytically, and applications to our heat pump system.

So I checked what I have already written – and I discovered a series which does not show up as such in various lists, tags, categories:

[2014-12-14] Cistern-Based Heat Pump – Research Done in 1993 in Iowa. Pioneering work, but the authors dismissed a solar collector for economic reasons. They used a steady-state estimate of the heat flow from ground to the tank, and did not test the setup in winter.

Cistern-Based Water-Source Heat Pump System Design, 1993[2015-01-28] More Ice? Exploring Spacetime of Climate and Weather. A simplified simulation based on historical weather data – only using daily averages. Focus: Estimate of the maximum volume of ice per season, demonstration of yearly variations. As explained later (2017) in more detail I had to use information from detailed simulations though – to calculate the energy harvested by the collector correctly in such a simple model.

Simple simulations of volume of ice[2015-04-01] Ice Storage Challenge: High Score! Our heat pump created an ice cube of about 15m3 because we had turned the collector off. About 10m3 of water remained unfrozen, most likely when / because the ice cube touched ground. Some qualitative discussions of heat transport phenomena involved and of relevant thermal parameters.

Ice formation during the 'ice storage challenge'[2016-01-07] How Does It Work? (The Heat Pump System, That Is) Our system, in a slide-show of operating statuses throughput a typical year. For each period typical temperatures are given and the ‘typical’ direction of heat flow.

System in September - typical operations conditions[2016-01-22] Temperature Waves and Geothermal Energy. ‘Geothermal’ energy used by heat pumps is mainly stored solar energy. A simple model: The temperature at the surface of the earth varies sinusoidally throughout the year – this the boundary condition for the heat equation. This differential equation links the temporal change of temperature to its spatial variation. I solve the equation, show some figures, and check how results compare to the thermal diffusivity of ground obtained from measurements.

Measured 'wave' and propagation time[2016-03-01] Rowboats, Laser Pulses, and Heat Energy (Boring Title: Dimensional Analysis). Re-visiting heat transport and heat diffusion length, this time only analyzing dimensional relationships. By looking at the heat equation (without the need to solve it) a characteristic length can be calculated: ‘How far does heat get in a certain time?’

Temperature waves in ground - attenuation length of about 10 meters[2017-02-05] Earth, Air, Water, and Ice. Data analysis of the heating season 2014/15 (when we turned off the solar/air collector to simulate a harsher winter) – and an attempt to show energy storages, heat exchangers, and heat flows in one schematic. From the net energy ‘in the tank’ the contribution of ground can be calculated.

Energy storage, heat exchangers, heat flow[2017-02-22] Ice Storage Hierarchy of Needs. Continued from the previous post – bird’s eye view: How much energy comes from which sources, and which input parameters are critical? I try to answer when and if simple energy accounting makes sense in comparison to detailed simulations.

Hierarchy of needs - ambient energy in ice months[2017-05-02] Simulating Peak Ice. I compare measurements of the level in the tank with simulations of the evolution of the volume of ice. Simulations (1-minute intervals) comprise a model of the control logic, the varying performance factor of the heat pump, heat transport in ground, energy balances for the hot and cold tanks, and the heat exchangers connected in series.

Simulations of brine and tank temperature and volume of ice, based on system state in 1-minute intervals.(Adding the following after having published this post. However, there is no guarantee I will update this post forever ;-))

[2017-08-17] Simulations: Levels of Consciousness. Bird’s Eye View: How does simulating heat transport fit into my big picture of simulating the heat pump system or buildings or heating systems in general? I consider it part of the ‘physics’ layer of a hierarchy of levels.

Simulation - levels of consciousness

Simulating Peak Ice

This year ice in the tank was finally melted between March 5 to March 10 – as ‘visual inspection’ showed. Level sensor Mr. Bubble was confused during the melting phase; thus it was an interesting exercise to compare simulations to measurements.

Simulations use the measured ambient temperature and solar radiation as an input, data points are taken every minute. Air temperature determines the heating energy needed by the house: Simulated heat load is increasing linearly until a maximum ‘cut off’ temperature.

The control logic of the real controller (UVR1611 / UVR16x2) is mirrored in the simulation: The controller’s heating curve determines the set temperature for the heating water, and it switches the virtual 3-way valves: Diverting heating water either to the hygienic storage or the buffer tank for space heating, and including the collector in the brine circuit if air temperature is high enough compared to brine temperature. In the brine circuit, three heat exchangers are connected in series: Three temperatures at different points are determined self-consistently from three equations that use underground tank temperature, air temperature, and the heat pump evaporator’s power as input parameters.

The hydraulic schematic for reference, as displayed in the controller’s visualization (See this article for details on operations.)

The Coefficient of Performance of the heat pump, its heating power, and its electrical input power are determined by heating water temperature and brine temperature – from polynomial fit curves to vendors’ data sheet.

So for every minute, the temperatures of tanks – hot and cold – and the volume of ice can be calculated from energy balances. The heating circuits and tap water consume energy, the heat pump delivers energy. The heat exchanger in the tank releases energy or harvests energy, and the collector exchanges energy with the environment. The heat flow between tank and ground is calculated by numerically solving the Heat Equation, using the nearly constant temperature in about 10 meters depth as a boundary condition.

For validating the simulation and for fine-tuning input parameters – like the thermal properties of ground or the building – I cross-check calculated versus measured daily / monthly energies and average temperatures.

Measurements for this winter show the artificial oscillations during the melting phase because Mr. Bubble faces the cliff of ice:

Simulations show growing of ice and the evolution of the tank temperature in agreement with measurements. The melting of ice is in line with observations. The ‘plateau’ shows the oscillations that Mr. Bubble notices, but the true amplitude is smaller:

2016-09 - 2017-03: Temperatures and ice formation - simulations.

Simulated peak ice is about 0,7m3 greater than the measured value. This can be explained by my neglecting temperature gradients within water or ice in the tank:

When there is only a bit of ice yet (small peak in December), tank temperature is underestimated: In reality, the density anomaly of water causes a zone of 4°C at the bottom, below the ice.

When the ice block is more massive (end of January), I overestimate brine temperature as ice has less than 0°C, at least intermittently when the heat pump is turned on. Thus the temperature difference between ambient air and brine is underestimated, and so is the simulated energy harvested from the collector – and more energy needs to be provided by freezing water.

However, a difference in volume of less than 10% is uncritical for system’s sizing, especially if you err on the size of caution. Temperature gradients in ice and convection in water should be less critical if heat exchanger tubes traverse the volume of tank evenly – our prime design principle.

I have got questions about the efficiency of immersed heat exchangers in the tank – will heat transfer deteriorate if the layer of ice becomes too thick? No, according also to this very detailed research report on simulations of ‘ice storage heat pump systems’ (p.5). We grow so-called ‘ice on coil’ which is compared to flat-plate heat exchangers:

… for the coil, the total heat transfer (UA), accounting for the growing ice surface, shows only a small decrease with growing ice thickness. The heat transfer resistance of the growing ice layer is partially compensated by the increased heat transfer area around the coil. In the case of the flat plate, on the contrary, also the UA-value decreases rapidly with growing ice thickness.


For system’s configuration data see the last chapter of this documentation.

Mr. Bubble Was Confused. A Cliffhanger.

This year we experienced a record-breaking January in Austria – the coldest since 30 years. Our heat pump system produced 14m3 of ice in the underground tank.

The volume of ice is measured by Mr. Bubble, the winner of The Ultimate Level Sensor Casting Show run by the Chief Engineer last year:

The classic, analog level sensor was very robust and simple, but required continuous human intervention:

Level sensor: The old way

So a multitude of prototypes had been evaluated …

Level sensors: The precursors

The challenge was to measure small changes in level as 1 mm corresponds to about 0,15 m3 of ice.

Mr. Bubble uses a flow of bubbling air in a tube; the measured pressure increases linearly with the distance of the liquid level from the nozzle:


Mr. Bubble is fine and sane, as long as ice is growing monotonously: Ice grows from the heat exchanger tubes into the water. The heat exchanger does not float due to buoyancy, as it is attached to the supporting construction. The design makes sure that not-yet-frozen water can always ‘escape’ to higher levels to make room for growing ice. Finally Mr. Bubble lives inside a hollow cylinder of water inside a block of ice. As long as all the ice is covered by water, Mr. Bubble’s calculation is correct.

But when ambient temperature rises and the collector harvests more energy then needed by the heat pump, melting starts at the heat exchanger tubes. The density of ice is smaller than that of water, so the water level in Mr. Bubble’s hollow cylinder is below the surface level of ice:

Mr. Bubble is utterly confused and literally driven over the edge – having to deal with this cliff of ice:

When ice is melted, the surface level inside the hollow cylinder drops quickly as the diameter of the cylinder is much smaller than the width of the tank. So the alleged volume of ice perceived by Mr. Bubble seems to drop extremely fast and out of proportion: 1m3 of ice is equivalent to 93kWh of energy – the energy our heat pump would need on an extremely cold day. On an ice melting day, the heat pump needs much less, so a drop of more than 1m3 per day is an artefact.

As long as there are ice castles on the surface, Mr. Bubble keeps underestimating the volume of ice. When it gets colder, ice grows again, and its growth is then overestimated via the same effect. Mr. Bubble amplifies the oscillations in growing and shrinking of ice.

In the final stages of melting a slab-with-a-hole-like structure ‘mounted’ above the water surface remains. The actual level of water is lower than it was before the ice period. This is reflected in the raw data – the distance measured. The volume of ice output is calibrated not to show negative values, but the underlying measurement data do:

Only when finally all ice has been melted – slowly and via thermal contact with air – then the water level is back to normal.

In the final stages of melting parts of the suspended slab of ice may break off and then floating small icebergs can confuse Mr. Bubble, too:

So how can we picture the true evolution of ice during melting? I am simulating the volume of ice, based on our measurements of air temperature. To be detailed in a future post – this is my cliffhanger!

>> Next episode.

Cistern-Based Heat Pump – Research Done in 1993

One of the most recent search terms on this blog was: ‘cistern for water source heat pump’. I wanted to double-check and searched for this phrase myself.

This was the first Google Search result:

Cistern-Based Water-Source Heat Pump System Design

… a research paper that had been available for download at the website of Iowa Energy Center at [*].

Cistern-Based Water-Source Heat Pump System Design, 1993


A considerable amount of research has been done regarding ground loop heat pump systems which are underground piping networks that extract heat from or dissipate heat to the ground and are coupled with a ground-source heat pump to greatly increase efficiencies for the heating and cooling cycles of the heat pump. The high costs incurred by home owners for installation of such a system is currently a deterrent to their implementation. This paper explores the feasibility of utilizing a submerged concrete water storage vessel, known as a cistern, as a cost effective alternative for storing and transferring geothermal energy for ground-source heat pump systems.

This work was been done as early as in 1993! The authors did theoretical modelling of the expected heat transfer, built a prototype connected to a home, and monitored performance for some weeks.

[For European readers – you will need this:]

They built a working prototype which resembles our heat pump system in some aspects – but there is one essential difference: They did not use a solar / air collector as they considered its contribution not essential. Experiments were done in spring, and future performance monitoring for a whole season had been announced in the paper. But the document was called a final report – so I assume the follow-up project had not been started.

Re-use existing infrastructure: Thousands of cisterns in the midwestern sector of the United States were built about 100 years ago. They were abandoned when home owners got access to running water. It seems that most of these vessels are still in good shape if filled with water all the time. Untapped potential!
We have re-purposed our useless root cellar, and we work with clients who want to re-use cesspits or cisterns. Here is an American home owner’s photo story on her slightly creepy cistern, and from this article I learned those cisterns are often located under the porch – exactly the idea we have come up with when thinking about heat sources.

Kenworthy Hall Kitchen and Cistern

Cistern in Alabama (Wikimedia).

DIY approach: Adams et al. provide a detailed information on prices and services required and they suggest that home owners could install it themselves. Re-purposing an existing vessel is more economic than building any of the standard heat sources – slinky-type ground source collectors, boreholes, or ground-water wells. This is still true today.
The authors said they had already several requests from local home owners who were interested in installing a pilot system.

Historic American Buildings Survey Lester Jones, Photographer February 28, 1940 CISTERN DETAIL AT REAR OF HOUSE - Lemee House, 310 Jefferson Street, Natchitoches, Natchitoches HABS LA,35-NATCH,6-4

Cistern in Louisiana (Wikimedia).

The pilot home’s floor space was about 60 m2 (640 ft2). The research paper includes a detailed home energy audit, similar to the one home owners need to provide when building or selling a house today in Austria. The design heating load – calculated from the building’s heat losses and the difference between the standard room temperature and the minimum ambient temperature – was about 7,6 kW (25.900 Btu/hour).
Since the test site was at 43° latitude, so 5° south to my home village, I suppose the climate is not extremely different or perhaps milder. Here the minimum daily ambient temperatures are about -13°C. In the past 20 years we have encountered this temperature on a single day; so this is a worst case estimate and the typical heating load in winter is much lower. Heating loads are used for comparing building standards, and the heating load is quite high given the small area. A modern insulated building with a 8 kW heating load would be 3 or 4 times larger. Those 8 kW accidentally match our theoretical load (for about 185m2 floor space) – so the size of the heat source should be comparable.

Photocopy of photograph (from Iowa State University Library, Special Collections) Photographer unknown ca. 1911-1926 SOUTH FRONT AND WEST SIDE - Iowa State University, Farm House HABS IOWA,85-AMES,2-5

I wondered how historical buildings in Iowa look like. This farm house is today situated on the campus of Iowa State University (Wikimedia).

The available cistern had a volume of 4200 gallons / 16m3 – this is about the right size for a house with 8 kW of heat losses. The authors state that the pilot building could be heated for 21 days, based on an heat extraction power of 9.000 Btu/hour. This is based on a heating power of a ton (3,5 kW) which is less then half of the design load. I think this is the heat load obtained from their experiment – venting the house to ambient temperature in early April.

The latent heat of water is 92,7 kWh/m3 so about 1.400 kWh can be gained in total. At an worst case load of 7,6 kW and a heat pump’s coefficient of performance  of 4, those 1400 kWh would be depleted after 246 hours, that is about 10 days. This is still not a bad value, and you would rather use some emergency heating system (electrical or stove) than building a bigger tank.

Heat pump and heat distribution: The heating system used in this project was a water-air heat pump; the paper contains calculation of the detailed design of the ductwork. The source side of the system is similar to any other water-source heat pump. This seems to be the successor product family.
Heat is transferred by a solution 20% polypropylene glycol in water, providing frost resistance for temperatures greater than -20 F (-11°C). The target side is an air ventilation system – rather uncommon in Austria as here we use mainly floor heating loops.

It was planned to use the ice or cold water created in winter for cooling in summer. This is the same idea we use – it is an added value you get for free as long as you don’t cool the floor below the dew point.

Adams et al.’s heat exchanger used in the cistern was made from copper. They calculated heat transfer for copper pipes versus PE plastic pipes (p.91/92 of the PDF) – and the length of copper pipes would be about 1/3 to 1/4 of plastic pipes. We have picked plastic pipes as they allow for rather easy and flexible installation – and perhaps for future 3D printing of the design :-)

Water to Air Heat Pump

Water to Air Heat Pump – bigger than water-to-water heat pumps.

Theoretical modelling of heat transfer and size of the heat source: Adams et al. have made an estimate of the heat flow from ground to their cistern. Their goal was to evaluate if an underground vessel would be sufficient as a single heat source. They also wondered if the surface area of the cistern could be compared with the surface area of typical vertical heat exchanger ground loops.

They calculated the steady-state heat flow between a cylinder and the surrounding ground, taking into account the heat conductance of the materials and a assuming a constant temperature difference of 15 F (8°C). Their calculated flow is of the same order of magnitude as the heat extracted from the source in their experiments (done in April). As the authors said, this is a very rough first estimate, and calculations are tedious and involve large uncertainties.

We did a numerical simulation of the dynamic change of the temperature distribution in ground, based on weather data gathered at least every hour. Calculating the dynamic heat flow from the temperature gradient at the interface between tank and ground results in a lower heat transfer – in agreement with our own experiments that now cover two full seasons. Thus ground should not be over-estimated – the power ‘released’ by ground on average is about half of the ballpark numbers used for geothermal ground loops.

Unterirdische Zisterne

The pilot system described in the paper uses a cylindrical cistern – perhaps similar to modern ones, such as this (Wikimedia).

Solar collector versus ground energy: Heat transfer from ground is relevant, so one must not insulate the tank. But the main contribution to the net flow to our tank originates from the solar / air collector. The tank is a buffer that bridges periods of time when the average ambient temperature is much below 0°C. Its direct contribution per interface area should not be compared to the heat exchanger loops’ surface area – it is lower than the typical heat transfer rate per area of ground harvested via ground loops (~20W/m2).

The solar collector was also dismissed for economic reasons – the authors of the 1993 papers calculated a payback time of 18 years. I was not able to identify the collector based on the brand name in the paper. The 1990s have been the golden era of DIY flat plate solar collectors in Austria – the time before companies had manufactured off-the-shelf products. In 2012 Austria is worldwide no. 2 terms of installed solar collector area per inhabitants – and is in top 8 even in absolute numbers, see p.12 of this report. I had once figured flat plat collectors are cheaper than evacuated vacuum tube collectors – but the latter are actually more popular in China. This report also shows that unglazed collectors are quite popular in the US. I wonder if Adams et al. had actually evaluated the same type of ribbed pipe collector we have picked because of superior heat transfer properties, and if such collectors had been considered too expensive in the US 20 years ago.

Monitoring and some adventures: The authors used a pragmatic approach I liked a lot: Do some theoretical estimates first to get a feeling for the numbers, and to evaluate the feasibility … then build a prototype and monitor it closely.
They used an Apple 2 computer for data acquisition, not so different from our first Mac SE. In some sense it is a good thing that they overestimated the contribution from ground as they might not have built the system otherwise.

Apple II plus

Apple II plus (Wikimedia)

This is an academic paper but the authors included some ‘tales from the field’, fighting with fluctuating output of sensors and …

To add to our problems, in trying to fix temperature transducers in the tank, we had left the tank open without water too long during a wet spell, and the tank wall broke [#] in due to the pressure difference between the tank and the ground. We tried to patch it the best we could (a novel could be written on this experience), and filled it with water again. However, the tank continued to leak and we had to continue to add water to it to maintain a desired level in the tank.

[#] I was surprised that wall if this cistern was just an inch thick – much thinner than modern rain water cisterns.

They factored in this unplanned addition of water – adding another Basic program (I wax nostalgic about the code listings in the paper!) that evaluates the balance of heat energy.

So in summary: Kudos to those pioneer engineers! If anybody reading this knows anything about follow-up projects done in Iowa in the 1990s, let met know! I haven’t researched the Iowa climate in detail. I cannot rule out that their heat source might have performed better than expected from experiments in middle Europe but I would be surprise if this cistern without a solar collector would have sustained a whole heating season.

I’d finally add our own schematic drawing again for comparison. The pilot system described in the 1993 paper does not user hot water tanks, and heating of hot tap water is not covered.

punktwissen heat pump system, water tank and solar collector as heat source

Our own system, built in 2012. Components also used in the experiment in 1993: Cistern as water tank, water-air-heat pumps, ductwork directly attached to it instead of buffer and hot water tank. More details in this post.


[*] After a migration to a new domain in 2018 the document is not available anymore. I’ve also contacted the owners of the new site who have confirmed this.