# 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:

So a multitude of prototypes had been evaluated …

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, and 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!

# 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 available for download at the website of Iowa Energy Center. (Note that the scanned PDF is 40MB in size.)

Abstract:

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: www.unitconversion.org.]

They built a working prototype which resembles ours in some aspects – but there is one essential difference: They did not use a solar 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.

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.

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.

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 till 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 a water-air heat pump had been used; 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 – 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 constant assumed 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 much lower heat transfer. This is in agreement with our own experiments that now cover two full seasons. Uncertainties can be reduced by modifying parameters such as the hard-to-calculate heat transfer coefficients of the ribbed pipe heat exchangers.

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 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 (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.

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.