More Ice? Exploring Spacetime of Climate and Weather.

I have become obsessed with comparing climate data for different regions in the world and in different years (space + time).

Finally I have found the tool I was looking for; now I can compare average Ice Days quickly – days with a maximum temperature < 0°C. In the first quarter of 2014 there were:

5 Ice Days in Vienna

compared to

68 Ice days Days in the Canadian prairie, in Regina, Saskatchewan, Canada.

It seems that a typical winter in Regina is about as grim as the winter in Europe in 1962/63, a 250 year event that has its own Wikipedia entry (DE version for Europe, EN article for UK). In this winter temperature was below 0°C for up to 120 days even in lowland areas. It was the most persistent cold since 1739. In Canada and Greenland temperatures were unusually mild in that season.

I am interested in the probability of extremely cold days in a row as this determines the size of the water tank to be used a heat source. The Austrian national weather service provides data since 1994. I used the daily average ambient temperatures as an input for a crude simulation – to determine the maximum volume of ice in the tank per year. So I did accounting of the energy in water tank:

  • How much energy is needed for space heating and hot water, based on ambient temperature and number of persons?
  • For a constant performance factor of 4 the heat extracted by the heat pump from the tank is 3/4 of this. The assumption is reasonable as long as the tank is big enough which means the tank temperature will not be lower than 0°C.
  • How much energy can be gained from ambient air? Air temperature needs to be some degrees higher than brine temperature which has typically less than 0°C in winter.
  • How big is the contribution of ground? If the tank would be fully frozen only this contribution would matter – then the system had turned into a geothermal one.

This was a much simpler exercise than detailed simulations I did for selected seasons before – based on and data taken every hour or even every 3 minutes. In the daily accounting approach, I did not take into account the detailed hydraulic schema, every switching of a valve or the temperatures ‘before’ and ‘after’ the heat exchangers in the tank and in the air. It also speeded up calculations to replace numerical simulations of the heat flow and the ‘temperature waves’ in the surrounding ground below the tank by simple estimates.

I compared the results to measured volume of ice for the past two seasons and to a detailed simulations for specific seasons. Since the maximum volumes of ice are approximately the same I consider the simple simulation good enough for providing an overview and some ‘feel’ about what different winters will result in.

Our tank is ~27m3 size in, thus allowing for ~25m3 of ice maximum as the volume is increased by 10% on freezing. It would have hit the limit in 1996 and 1997:

Volume of ice, water tank as a heat source of heat pump. Simulation for 1994-2013.
Volume of ice in the tank, determined by ambient temperature. The peak for 2005/2006 is in agreement with a ‘real’ detailed simulation, the peak for 2012/2013 with the measured value. The small peak for 2013 is still larger than the observed value as the simple simulation based on daily values only breaks down if the ‘lifetime’ of the ice peak is too small.

Every heat pump system has an option to switch to a heating element in case the heat source is exhausted. With air heat pumps, the ambient air simply gets too cold. Geothermal systems utilize a big volume of soil, so the source would be exhausted just as our tank when a large volume of soil is frozen. Limiting factors are the freezing point of brine and the thermodynamic properties of the refrigerant.

We would have used the heating element 2 times in 20 years for a few days. This could be prevented if the tank was built bigger; finally it boils down to an economic assessment:

  • Our house needs about 20.000 kWh per year of energy (hot water included) This is a conservative estimate – in the season 2013/14 we needed only 17.500 kWh.
  • As long as the tank is not frozen, the performance factor is 4 and thus 3/4 of this will be provided by ‘the environment’ / the tank: 15.000 kWh.
  • The remaining energy is the electrical energy consumed by the heat pump’s compressor: 5.000 kWh.
  • On a very cold day the heating energy is: 130 kWh (equivalent to 5,4 kW – so still below design heating load); about 98 kWh are extracted from the tank.
  • The tank contains about 2.000 kWh latent heat and can sustain about 20 very cold days.
  • The ‘ten year colds’ lasted for a few days more. Four more days would require about 500 kWh extra, by 1:1 heating.

I highlighted the essential numbers to be compared: Once in ten years, electrical heating energy would be higher by about 10%. On average (per year), this would add only  1%. 1% of the yearly utility bill’s total need to be compared to the costs of building a larger tank.

In an exceptional winter like season 1962/63 about two more months had to be sustained: Heating at worst case power for 60 days is equivalent to 7.800 kWh; and using a 1:1 heating element means an excess electrical energy of 5.850 kWh – those 3/4 of the total heating energy that would otherwise (before the tank is exhausted) be provided by ‘the environment’. This has to be compared to standard consumption for 250 years, that is: 250 times 5.000 = 1.250.000 kWh. Thus excess heating energy amounts to less than 0,5%.

One might argue that 250 years does not make sense as you might at best consider heating costs for one human being’s life time – and you might encounter such a season, or not. But after all, these numbers would just provide some way of comparing different heating systems – all of which would result in excessive heating costs in such a winter no matter what the fuel was.

20 Comments Add yours

  1. Just for fun .. I’m wondering what it costs you to run this system. I think you know that we heat exclusively with wood. It costs us about $1500 per year to heat about 2000 square feet. Let’s make it simple and say that it costs approximately $1.25 per sq foot to heat. I’m wondering if you have made the same determination for your place.

    1. Oops … I mean $0.75 per square foot! It’s been a long week. D

      1. elkement says:

        Our floor area is exactly the same: 185m2.
        Costs per year are about € 750 for space heating and hot water, so about $ 850, thus $ 0,425 / sq foot
        That’s based on about € 0,17 per kWh costs of electricity (energy, grid, taxes).
        This is half of what we paid for heating with natural gas before.

        But to rule out issues with financial markets and currencies, we should rather compare costs per kWh needed for heating. So heating energy for hot water should be subtracted (this would about 1/4 of the total energy in our case). Note that even then we are also comparing differences in climate and insulation.

        Do you know the caloric value of that wood you typically use and can you convert it into energy? I guess it is difficult to single out the part needed for hot water? Anyway, I would be be curious about the amount / volume of wood you need per year in whatever unit!

        Actually I had already considered to write a post about comparing costs!

        1. Interesting. Wow, you heat for approximately half of our cost … and with far less effort (no cutting, splitting, and hauling of wood). That’s impressive, really. We use approximately 6 cords of wood in a season, perhaps a bit more. A cord is a volume of wood of dimension 4X4X8 feet, 128 cu ft = 3.62 cu m.

          1. elkement says:

            Thanks a lot, Dave – I will do the math and learn some new units :-) … and you have given me an excuse for an upcoming – perhaps boring – post on the economics of heating! Your questions always add value to my posts!!

            1. I found a very nice table which provides values of heat per cord (millions of BTUs) for various types of wood. [Isn’t the internet an amazing thing?] We burn primary Red Oak.


          2. elkement says:

            (I had crafted this reply before I knew that you burn Red Oak – see the next reply below for the updated version of the estimate.)

            OK – I have found the heat value per cord, so I don’t have to convert volumes ;-)
            It depends on variety of wood, dryness, if the boiler can utilize recoverable heat: 15-20 million BTU (MMBTU) per cord.

            So a million BTU is 293 kWh, thus you need about
            6 cords x 15 MMBTU/cord x 293 kWh/MMBTU ~ 26370 kWh
            using 20 MMBTU/cord it would amount to ~ 35160kWh

            We need less than 20000kWh. As you say you might need more – and assuming your wood as a high combustion value – the difference might just compensate for the costs. So wood seems to be quite cheap in your place – but this is again comparing Austrian prices for electricity with US prices for wood. In Austria the operating costs of a heat pump are typically lower than costs for alternative fuels.
            So for the ultimate comparison we could also convert the energy you need into electricity that would be needed with a heat pump in your place. ‘The internet’ tells me that electrical power seems to be cheap in the US compared to other countries:
            But I am not sure if these prices are just market prices for energy or if this comprises really everything the home owner pays for (like metering services, grid).

            Anyway you know your electricity bill. For a very crude comparison you could divide your total heating energy by 4 (performance factor of heat pump) – this is the kWh of electrical power the heat pump would need, to be multiplied by your $ / kWh.

          3. elkement says:

            Thanks, Dave – I had already replied before in detail, using an average value from two other tables (15-20 MMBTU). If I now use the value for Red Oak from that table, about 24,6 MMBTU, the total energy is higher than what I had assumed before:

            6 cords x 24,6 MMBTU/cord x 293 kWh/MMBTU ~ 42250 kWh.

            This is a bit more than twice the energy we need per year. So per kWh your costs are similar. We now compare the Austrian costs of electricity to the US prices of wood.

            In order to compare your costs for wood with the hypothetical costs of a heat pump system, I’d need to know the effective price per kWh electrical energy.
            Assuming the heat pump has a coefficient of performance of about 4, you would need about 10000kWh electrical energy for heating.
            The link I added below implies that electricity is cheaper in the US than in Europe, but I am not sure if these prices do include all the costs on your electricity bill (energy+grid). If those $0,12 / kWh are total costs, then you’d end up with $0,12 x 10000 = $1200 … exactly what you pay for wood today!

            Things not considered: The performance factor of the heat pump depends on different things, e.g. heating hot water to a high temperature decreases it. On the other hand, I have not taken into account the efficiency of your stove which has to be less than 1. If it is, say 85%, then the heating energy to be generated by the heat pump would only the 85% of the heat value of your wood.

            1. All very interesting. I’ll check my last electric bill to see if I can locate a cost per kWh.

        2. elkement says:

          I have this brief introduction to US electricity bills – so it seems there are grid fees (called delivery fees) on top of those $0,12:
          So most likely you would end up with higher costs for the electrical power needed by the heat pump than what you pay for wood today. If the difference is not that dramatic, say 20%, then the efficiency of your stove would be important. If you would pay 20% more for electrical power, and if your stove would only deliver 80% costs would still be the same. As far as I know (but I don’t claim too much expertise in burning biomass) very efficient stoves have an efficiency of 80-90%.

  2. Interesting analysis. One additional thought came to mind while I was reading this, though. I wonder about the physical effects that would occur by having a significant volume of the water turn to ice. Would it tend to crush the internal pipes or, even worse damage the liner of the cistern? Not something you would like to find out through experiment for sure but still important questions. Something else–are there other ways to inject additional emergency heat into the cistern when ice conditions run to the extreme–an additional air supplied pump (Or perhaps that makes no economic sense), or maybe in some instances the ability to tap into geothermal (again, probably not as they would then be used as a primary I suppose).

    1. elkement says:

      Thanks, Maurice! Yes, this was a very important issue to consider when designing the details of the heat exchanger and supporting construction. Ice starts growing at the heat exchanger tubes – into the remaining water. There are no ‘spikes’ that would hurt the liner. There must not be one continuous ‘slab of ice’ that will cover the whole tank and would trap the remaining water. Here the trick is to use a very tiny ’emergency’ heater in the right place ;-) In addition the whole thing must be fixed and not allow for ‘floating’ of the ‘ice cube’.

      We would not inject heat into the cistern (except for that special tiny heater mentioned above, but it’s overall contribution is negligible) – we would just stop extracting heat from it in case it has been frozen to a certain extent. The contribution from ground is always positive in winter as the tank’s lid is insulated from cold air (and the tank should be underground, with a considerable part below depth of frost penetration); so the tank would get slightly warmer over time or at least not colder.

  3. Joseph Nebus says:

    I’m sorry, I’m still staggered thinking of the similarity between a typical Saskatchewan winter and an extraordinarily bad European one.

    1. elkement says:

      You’re right – I marveled at that for some time, too! It’s weird – but just knowing the numbers has not the same impact as knowing that this climate is similar to Europe’s worst every winter.

      BTW – I have discovered the significance of season 1962/63 while playing with historical German data – for 1950 and later. I saw that extended period of frost and wondered if this could be ‘typical’? Then I entered ‘winter 1962 1963’ into Google, not expecting too much…

    2. Michelle H says:

      The pair of these remarks made me grin a little (perhaps madly, given where I’m living).

      1. elkement says:

        ;-) Yes, my pick of a place with grim winter might have been influenced by one specific loyal reader. An Austrian refering to the harshest winter imaginable would otherwise choose Siberia. Now I need to check numbers for Siberia …

        1. Joseph Nebus says:

          Well, I went through my harshest winter last year, in mid-Michigan, but I didn’t compare it to Siberia or anywhere else. I think I mostly didn’t want to know how it compared.

  4. Michelle H says:

    I’ve been thinking about alternative energies in extreme climates like Regina, Saskatchewan, Canada. Habitation didn’t really begin here until imported heating fuels became readily available. The earliest settlers didn’t have very much wood for fuel to burn (if any), and some of their homes are interesting adaptations that relied on conservation. One thick-walled stone house I read about in the Regina area was built 3 stories tall, with the ground floor covered over in dirt on three sides. During the coldest days of winter the family living in the house would bring their farm livestock into the ground floor. The heat from the animals would help heat the house, and the family remained together on the floor above.

    Right now, like most North Americans, Canadian prairie dwellers have forgotten what living here was like before cheap and easy natural gas pipelines connected to their houses, fueling furnaces that run almost non-stop in extreme weather. The older homes have almost no insulation (i.e. built before 1990), but even new homes that are required to be better insulated by national building code regulations are energy-eaters in that most of them are too large to be conservatively heated.

    As for heat pumps… it might not work to build a water tank large enough to offset the cost of the system for use here. But, there are milder parts of Canada. One of the growing trends now is to install rain water collection tanks. The water is used for gardens, lawns, toilets. Municipal water is required for drinking and bathing. The tanks are primarily placed in new developments in heavily populated areas (like Toronto and surrounding suburbs) because existing city water supplies, sewer and storm drain systems cannot accommodate the increasing demands of expansion and growth. If I lived in eastern Canada, and had the means to install a grey-water collection tank, I’d be curious about combining it with a heat pump.

    1. elkement says:

      Thanks, Michelle – the story about the animal heaters is fascinating… I will have to google that :-)

      It is baffling that houses built before 1990 had barely been insulated, but it reminds what I learned about renewable energy usage in Iceland. Despite the abundance of geothermal energy they relied on oil for a long time – as oil was so cheap.

      Yes, a tank in your place would have to be enormous :-) I just checked the numbers for Toronto using that tool: On average they have about 50% ice days so it might work. I have once read about Chinook Winds in Canada – these would be perfect to melt the ice again quickly. We had such a storm and spell of warm weather, and you can harvest a huge amount of energy – especially when there is ice in the tank: Then the temperature of the tank stays at 0°C and the temperature difference to the ambient air is rather large and results it a large ‘heating power’ of the collector.

      I think combining the tank with a rain water collection tank is a great idea – one of our clients also uses the tank in both ways. It is designed larger so that the water required for toilets can be provided also when the tank starts to freeze (partially).

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