Data Kraken – the
tentacled tangled pieces of software for data analysis – has a secret theoretical sibling, an older one: Before we built our heat source from a cellar, I developed numerical simulations of the future heat pump system. Today this simulation tool comprises e.g. a model of our control system, real-live weather data, energy balances of all storage tanks, and a solution to the heat equation for the ground surrounding the water/ice tank.
I can model the change of the tank temperature and ‘peak ice’ in a heating season. But the point of these simulations is rather to find out to which parameters the system’s performance reacts particularly sensitive: In a worst case scenario will the storage tank be large enough?
A seemingly fascinating aspect was how peak ice ‘reacts’ to input parameters: It is quite sensitive to the properties of ground and the solar/air collector. If you made either the ground or the collector just ‘a bit worse’, ice seems to grow out of proportion. Taking a step back I realized that I could have come to that conclusion using simple energy accounting instead of differential equations – once I had long-term data for the average energy harvesting power of the collector and ground. Caveat: The simple calculation only works if these estimates are reliable for a chosen system – and this depends e.g. on hydraulic design, control logic, the shape of the tank, and the heat transfer properties of ground and collector.
For the operations of the combined tank+collector source the critical months are the ice months Dec/Jan/Feb when air temperature does not allow harvesting all energy from air. Before and after that period, the solar/air collector is nearly the only source anyway. As I emphasized on this blog again and again, even during the ice months, the collector is still the main source and delivers most of the ambient energy the heat pump needs (if properly sized) in a typical winter. The rest has to come from energy stored in the ground surrounding the tank or from freezing water.
I am finally succumbing to trends of edutainment and storytelling in science communications – here is an infographic:
(Add analogies to psychology here.)
Using some typical numbers, I am illustrating 4 scenarios in the figure below, for a system with these parameters:
- A cuboid tank of about 23 m3
- Required ambient energy for the three ice months is ~7000kWh
(about 9330kWh of heating energy at a performance factor of 4)
- ‘Standard’ scenario: The collector delivers 75% of the ambient energy, ground delivers about 18%.
- ‘Worse’ scenarios: Either collector or/and ground energy is reduced by 25% compared to the standard.
Contributions of the three sources add up to the total ambient energy needed – this is yet another way of combining different energies in one balance.
Neither collector nor ground energy change much in relation to the base line. But latent energy has to fill in the gap: As the total collector energy is much higher than the total latent energy content of the tank, an increase in the gap is large in relation to the base ice energy.
If collector and ground would both ‘underdeliver’ by 25% the tank in this scenario would be frozen completely instead of only 23%.
The ice energy is just the peak of the total ambient energy iceberg.
You could call this system an air-geothermal-ice heat pump then!
Continued: Here are some details on simulations.