Temperature profiles, in all different shapes and forms, form the basis of geothermal design, and it is really important to get familiar with them before proceeding in this course. Therefore, in this chapter, we will discuss them in great detail, so you know what they are and you have the required background information to dive into the underlying physics in the next chapters. Let’s get started!
Two types of profiles
As we discussed in Part 1.4, we can do geothermal simulations with different types of load profiles. On the one hand, we can do simulations with an hourly load profile, where the building load (or vice versa the ground load) is defined for every hour of the simulation period or we can rely on a monthly data resolution. Below, we will first explain the hourly temperature profile followed by the monthly one.
Hourly temperature profile
Below, a temperature profile is given for a 20 year period with an hourly resolution, meaning we get a temperature value at every hour of the simulation. As we discussed in Part 1.2 on the importance of borefield design, the horizontal dotted lines are our minimum and maximum allowed temperature limits and are constant. In this case, since we cross our maximum threshold, one could argue that this field is not designed correctly.
The other two lines, the blue and black lines, tell us something about our geothermal system. In general, we care about two things: the borehole wall temperature (which is the temperature of the ground directly touching our borefield) and our fluid temperature (since that will have an impact on the efficiency of our system, as discussed in Part 1.5). Of these two, the fluid temperature is the most important one.
In the profile above, two main trends are visible. We have on the one hand a seasonal variation since the profile has some sinusoidal behaviour, which is caused by heat being extracted from the field in winter and being injected in summer, respectively cooling down and heating up the borefield. On the other hand, we clearly see a temperature drift towards lower temperatures, caused by the imbalance, the difference between heat injection and extraction. This means that, by convention, when we have more extraction than injection, the imbalance will be negative.
Perhaps you will find that in your simulation (as also in the example above) the difference between the fluid and borehole wall temperature is not clearly visible. Therefore, below, a close-up of one summer month is shown.
Here, you can clearly see the spikes in temperature, where the fluid temperature deviates from the borehole wall temperature. Since this is a close-up in summer, we see that our average fluid temperatures are higher than our ground temperatures. This is because we are now injecting heat into the ground, as heat always flows from a warm to a cold location (which is also why your hot cup of coffee cools down on the table). In winter, you’ll find that the fluid temperatures are lower than the ground temperatures.
Perhaps you have already seen that at some moments, the fluid and the borehole wall temperature overlap. This is because at these instances, there is no injection or extraction demand, so the fluid temperature is undefined. You can think about this as follows: when you are not exchanging energy with your borefield, you are not looking at the temperatures and hence you have no idea what they are (and you also do not care). In GHEtool, we use the convention that, when there is no load, the fluid temperature equals the borehole wall temperature.
This however is not 100% accurate, since it ignores the thermal inertia of the fluid. This means that, if we have a fluid at a certain temperature and we stop heating or cooling it, the temperature does not suddenly drop, but it will change gradually to become in equilibrium with the environment (in this case the borehole wall temperature). At the time of writing, this thermal inertia is not included in these graphs and we will revisit them in the next chapters.
Monthly temperature profile
For faster calculations, it is possible to work with monthly load profiles. Here, the temperature profile has 4 different lines, the borehole wall temperature, just as before, together with three different fluid temperatures. In general the same two trends are visible in this example: a seasonal variation as well as a (slight) imbalance towards cooler temperatures.
The close-up of the first five years below makes it easier to distinguish between the different fluid temperatures. When you simulate with an hourly load, at every hour there is either heat extraction or heat injection, but at a monthly time scale, both can occur during the same month.
If you for example take a look at the spring month May: it can happen that the beginning of the month still has some heating demand but towards the end there is more demand for cooling. Therefore, each month can have both a temperature for peak heating and peak cooling demand, where the temperatures during heating are lower than the borehole wall temperature and the ones during cooling are warmer than the borehole wall.
Now, the last temperature is the green line which is the average fluid temperature during baseload. In contrast to the peak loads (where you can have both heating and cooling in the same month), every month only has one net resulting ground load, i.e. in every month there is only either a net extraction or injection of heat. If you would take away all the peak powers and just work with the energy balance, the temperature profile would look like the green line.
Another way to look at this baseload temperature is that it is the best case situation.
Imagine the case where you have a building with 730 kWh of heating demand in a certain month. On a monthly scale, you can deliver this energy to the building either with a constant 1 kW baseload power – a month has 730 hours – or with 2 hours at 365 kW. Both will deliver the same energy to the building, but the peak temperature during heating will be significantly lower in the second case.
If you maximise peak shaving and shifting and install quite a lot of buffer vessels, you can lower the peak power, until, theoretically, you end up in the best case situation of the baseload temperature.
At first, this might seem a little bit strange, but this baseload temperature can be interpreted as an average fluid temperature during your simulation period and it is also warmer than the borehole wall temperature during summer (because there is more energy injected in the ground than extracted) and vice versa during winter.
Borefield quadrants
Before diving into the physics and discussing how the inputs we discussed in part one of this course give rise to the temperature profiles above, let us take a closer look at them.
Imagine we have the temperature profile below, which has a negative imbalance and is clearly limited by the maximum temperature limitation. This could for example be the case of an auditorium or a high-end residential building, where the yearly demand for heating is typically larger (leading to the negative imbalance) but the peak power in cooling is actually the limiting factor.
In the profile below, another imbalance can be seen. This could for example be an office building (or even a commercial building like shops) where there is more cooling than heating demand on a yearly basis, causing a positive imbalance, limiting the design again by the maximum temperature.
Another profile with a negative imbalance, is given below. Here, the critical point is the minimum temperature during peak extraction at the last year of the simulation period. This could for example be a residential building where heating (and domestic hot water demand) makes the borefield extraction dominated.
The last situation that can occur, is given below. Here there is a positive imbalance, but the borefield is still limited by a high extraction load. In rather cold countries, this could occur as well for the office case (especially if you have active cooling and a maximum limit higher than 17°C), where the ground temperatures are rather low in the beginning.
All those four different options, can now be visualised as follows.
In the image above, the four different cases are structured in a 2×2 grid based on whether they are designed (or limited) by the minimum and maximum temperature and whether they experience that limit in the first or the last year of the simulation period. These are called the borefield quadrants.
In the figure above, quadrants 1 and 4 are coloured green whereas 2 and 3 are coloured blue. This categorisation is based on the imbalance since both 1 and 4 have a negative imbalance and 2 and 3 have a positive imbalance. When sizing a borefield, it is not a priori known in which of the 4 quadrants you will end up, so in theory you (or at least the algorithm) should check all of them. Now, based on the imbalance, this search space could be reduced to only 2 options.
Imagine you have a borefield with a negative imbalance, then we are sure that the borefield will never be in quadrant 2 and 3. To prove this, let us use proof by contradiction and hypothesise the following: imagine the borefield would be limited by the minimum temperature in the first year. Due to the imbalance, we know the borefield will be cooler the next year, so the first year can never be the critical point. This is in contradiction with our hypothesis, so it cannot be that the borefield falls in quadrant 3.
Let us now take a look what these borefield quadrants can teach us about our borefield.
A priori insights
The key advantage of categorising borefields into different borefield quadrants is that it allows you to reason about certain geothermal questions without the need for further calculations. Below, we answer three common questions purely by considering the borefield quadrants.
When is imbalance/regeneration relevant for investment cost?
It is often said that regeneration, with the purpose of reducing the imbalance, reduces borefield investment costs, but this is not always the case. If a borefield falls into quadrant 1 or 3, where the design limitation occurs in the first year of operation, imbalance does not pose a problem. In contrast, in quadrants 2 and 4, reducing imbalance through regeneration leads to a smaller borefield, as the system is designed based on the final year of the simulation, when accumulated imbalance has the greatest impact.
When is drilling deeper advantageous?
For buildings with high heating demand, drilling deeper can be beneficial because ground temperatures increase with depth (as we discussed in Part 1.3). This means that borefields in quadrants 3 and 4 can benefit from deeper boreholes, while quadrants 1 and 2 will not, as they are designed primarily for heat injection rather than heat extraction.
When is active cooling advantageous?
Active cooling can be a highly effective way to optimise investment costs, but only for borefields designed to handle high heat injection demands. With active cooling, the temperature limitation shifts from typically 16–17°C (for passive cooling) to 25°C or higher, allowing for a smaller borefield and thus lower investment costs. This is beneficial in quadrants 1 and 2, but not in quadrants 3 and 4.
Conclusion
In this chapter, we discussed the two types of temperature profiles when working with borefield design: hourly temperature profiles and monthly ones. Based on some general characteristics intrinsic to each profile (namely the imbalance and the peak temperatures) the borefields were categorised in quadrants. These borefield quadrants give us extra insight in the behaviour of the system without the need for extensive calculation.
In our next chapter, we will explore what is behind these temperature profiles and we will introduce the important concept of the effective borehole thermal resistance.
Questions
References
- Peere, W., Picard, D., Cupeiro Figueroa, I., Boydens, W., and Helsen, L. (2021). Validated combined first and last year borefield sizing methodology. In Proceedings of International Building Simulation Conference 2021. Brugge (Belgium), 1-3 September 2021. https://doi.org/10.26868/25222708.2021.30180