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Required inputs: Ground properties

Before we start with the actual sizing of borefields, it is important to know which information is required and where it can be found. In this chapter, the focus will be on the ground properties.


Ground properties

Since borefields are basically ground heat exchangers, it is rather trivial that the ground properties play an important role in its design. Geologists have many different ways to classify soil, including grain size, chemical composition, or mineralogical characteristics. However, for borefield design, only two key parameters are required:

  1. Thermal conductivity – how well the soil conducts heat
  2. Volumetric heat capacity – how well the soil stores heat

Both will be explained below.

Thermal conductivity

Thermal conductivity measures how effectively the ground conducts heat. Borefields interact both with the ground between boreholes and the surrounding, infinite ground. A borefield located in a location with a higher thermal conductivity allows for more efficient heat exchange with its surroundings.

For example, if you have a borefield with a significant imbalance (i.e. a borefield that cools down year after year), it is better to have good ground conductivity, so that the local thermal distortion can be dissipated faster.

Volumetric heat capacity

Volumetric heat capacity describes how effectively the ground can store heat. It represents the amount of energy required to increase the temperature of a certain volume of ground by 1°C, and can be thought of as the borefield’s ability to function as a heat battery. When we mentioned before that borefields are a seasonal thermal energy store, this was the reason why.

If a borefield has an almost zero imbalance (meaning the ground temperature stays constant over time), a high volumetric heat capacity is desirable, as this allows the borefield to act as a seasonal thermal energy storage (STES) system. In such cases, low thermal conductivity is also beneficial as it minimises heat loss to the environment.

In addition to thermal conductivity and volumetric heat capacity, other measures are used to quantify the thermal properties of the ground, such as thermal diffusivity and hydraulic conductivity.

Thermal diffusivity

The thermal diffusivity, $\alpha$, of a material is defined as its ability to conduct heat relative to its ability to store. It and is defined as follows: $$\alpha=\frac{\lambda}{C_v}$$where $\lambda$ is the ground thermal conductivity in (W/(mK)) and $C_v$ is the volumetric heat capacity in (J/(m³K)). The units of the thermal diffusivity are therefore (m/s²). Thermal diffusivity, thermal conductivity and volumetric heat capacity can all be used interchangeably.

Hydraulic conductivity

The hydraulic conductivity $K$ of the ground is important for groundwater flow, as it determines the velocity of flow (m/s) through the ground. It depends on the porosity of the material, which is expressed as intrinsic permeability ($k$ in m²), as well as the density and viscosity of the fluid. Hydraulic conductivity can be defined horizontally or vertically, depending on the flow rate of interest.

For borefield design, this is not immediately of interest, but it definitely plays a role in more advanced geothermal simulations.

Example data

The properties of the ground vary significantly depending on the location of the project. The table below shows the thermal conductivity and volumetric heat capacity of different soil and rock types, as reported in the literature.

Ground properties
From (Andújar Márquez et al., 2016),  https://doi.org/10.3390/s16030306

A few key observations:

  • Even within the same soil type, the thermal conductivity range varies widely. This is due to geological differences within each category affecting ground properties.
  • The thermal properties of granular soils (e.g. gravel, sand, silt and clay) are significantly influenced by water saturation. The spaces between soil particles can be filled either with air, which is an insulator, or with water, which has high thermal conductivity and heat capacity. Consequently, water-saturated soils have much higher thermal conductivity than dry soils.
Ground properties are highly specific to the case and location. It can often be difficult to obtain precise data, particularly with regard to the degree of water saturation. For the most accurate information, consult your local geological institute or authority. We have provided links to some of these institutes at the end of this chapter.

For the most accurate results, you can perform a Thermal Response Test. This involves taking an in situ measurement of the thermal properties of your ground, as well as the undisturbed ground temperature. To conduct a TRT, you need to drill a borehole at your project location to the desired final design depth. Next, a constant load is applied to the borehole. Based on the temperature measurements, the ground’s thermal conductivity, undisturbed ground temperature, and sometimes the volumetric heat capacity can be inferred.
We will cover TRT analysis in detail later, once the necessary physics has been covered.

Illustration of a thermal response test (TRT).
Illustration of a thermal response test (TRT). (Source: https://whelveenergy.gr/en/thermal-response-test)

Ground temperature

Another crucial parameter in borefield design is ground temperature, specifically the undisturbed ground temperature. This is the initial average temperature of the ground alongside the borehole, and it is used as a starting point for any geothermal simulation. If your undisturbed ground temperature is 11°C, for example, your borefield simulation will start at 11°C; if it is 13°C, it will start at 13°C. In the latter case, all temperatures (both fluid and ground) will be 2°C higher.

The undisturbed ground temperature can be measured using a Thermal Response Test (TRT), or inferred from ground thermal conductivity and geothermal heat flux. Using this linear ground temperature model, the undisturbed ground temperature can be calculated based on the temperatures at the start and end of the borehole (either an input or result of sizing).

This temperature gradient is caused by geothermal heat flux from the Earth’s core towards the crust. However, this heat is not evenly distributed across the globe, with some regions experiencing a higher or lower geothermal gradient and resulting ground temperature.
Temperature gradient
From (Akkuraja and Roy, 2011), https://doi.org/10.1016/j.pce.2011.01.004

The geothermal gradient $\Delta T$ in (°C/100m) can either be provided directly or it can be calculated based using the geothermal heat flux $q$ in (W/m²) and the thermal conductivity $\lambda$ in (W/(mK)). The gradient can then be calculated as follows: $$\Delta T = \frac{\dot{q}}{100\lambda}$$When the gradient $\Delta T$ is known as well as the ground surface temperature $T_s$, the temperature $T$ at depth $x$ can be calculated as: $$T(x)=\frac{1}{2}\cdot\left(T_s+\frac{x\cdot\Delta T }{100}+T_s \right) = T_s+\frac{x\cdot\Delta T}{200}$$

The undisturbed ground temperature $T_u$ for a borehole starting at $x=D$ to $x=H$ is hence given as: $$T_u= \frac{T(D)+T(H)}{2} = T_s + \Delta T\cdot\frac{D+H}{200}$$

Assuming a constant, linear increase in temperature with depth is not always accurate, particularly in densely populated areas or older cities.

As shown in the figure below, the average ground temperature rises when a city is built on top of it (second graph). This is due to the urban heat island effect, whereby heat from buildings, roads and pavements becomes trapped and warms up the entire city. Over time, this increased temperature penetrates the ground, creating a temperature ‘blob’ that can extend up to 100 metres deep.

Effect on the temperature gradient
From: https://www.e-education.psu.edu/earth103/node/752

This temperature disturbance is particularly significant for buildings with high cooling requirements, as a higher initial temperature brings them closer to the maximum temperature limit. While the traditional linear temperature model suggests that deeper drilling is not beneficial for cooling, in some urban areas it may actually be necessary to reach cooler ground temperatures for efficient cooling.

As ground temperature is always subject to some degree of uncertainty, it is highly recommended, especially for large projects, to conduct a TRT in order to measure the initial, undisturbed ground temperature.

Ground data in GHEtool

GHEtool provides two ways to enter ground properties:

  1. Layer-by-layer data input
  2. Homogeneous ground properties assumption

Since GHEtool internally assumes one averaged ground layer, both methods can yield the same result.

Layered data

The most accurate and reliable way to enter your ground data is to use the layered option in GHEtool Cloud. Here, you can enter your ground properties layer by layer, along with the thickness of each layer. GHEtool will then automatically calculate the correct thermal properties for each design based on your buried borehole depth. When calculating the required borehole depth to stay within the design limits, entering the ground properties layer by layer will help you to achieve more accurate results.

Homogeneous data

If you need to perform a quick calculation, entering all the ground layers can be time-consuming. Therefore, you can input your ground data using the homogeneous assumption. In this case, you simply enter one value each for ground thermal conductivity and volumetric heat capacity, which will be used for all borefield sizes.
Please note that the homogeneous data entered will always be an average of multiple ground layers at a given depth. If you use a borefield with a different borehole depth to that used to calculate these average parameters, the results may be inaccurate. Therefore, if you change the borehole depth (or allow it to be calculated using the ‘Calculate required borehole depth’ option), it is essential to double-check your ground properties.

Conclusion

This chapter discussed the ground properties required for a geothermal simulation. The ground’s thermal conductivity and volumetric heat capacity, as well as the undisturbed ground temperature, are all required. The next chapter will focus on thermal demand.

Questions

Given a surface ground temperature of 10°C, a geothermal heat flux of 0.06 W/m² and a ground thermal conductivity of 3 W/(m·K), what is the ground temperature at a depth of 100 m? Assume a linear temperature gradient.
Using the same data as above, calculate the undisturbed ground temperature if the borehole starts 10 metres below the surface.
I have a very shallow borefield, only 40 m deep. The initial measurement of ground conductivity was taken at the end of the rainy season. What effect could this have on the accuracy of the test, and what are the consequences if my borefield has a strong imbalance?

References

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