### Development of a soil thermal conductivity map of Bavaria for design of shallow geothermal applications

*Toshihiko Momose*

^{1}, Marcellus Schluze

^{1}, Bernhard Wagner

^{1}

^{1}Bayerisches Landesamt für Umwelt

P 8.1

*in*Geothermie und Geocooling

**Introduction**

Soil thermal conductivity (*λ*) is a primary property determining the heat extraction potential of ground heat exchangers (GHE). In the context of the EU co-financed project “Information Offensive Geothermal Energy (IOGI)” Bavarian Environment Agency – Geological Survey creates a soil map of the *λ *values in Bavaria in the scale of 1:25 000, to provide an overview of the spatial efficiency for horizontal GHE. The model for the *λ* estimates will allow the prediction of heat extraction potential for near surface geothermal applications and thus is a major milestone of the project.

**Materials and methods**

Twenty-one Bavarian soils with a large variety of soil textures were selected for the *λ* measurements. For each soil, seven samples with different water content were prepared at a constant dry bulk density and their *λ *data were measured by the heat-probe method. Additionally, the 21 soils were tested for physical properties, such as grain size distribution and mineral composition, required for model development.

**Results and discussion**

The *λ* values increase with the saturation degree (*S*) for each soil. We find that the increase in *λ* over log *S* values can be divided into two categories at a particular *S* value (*S*_{p}). In the range of *S* < *S*_{p}, the *λ** *values keep almost the same to that at dry conditions (*λ*_{dry}). For *S* > *S*_{p}, the *λ* values are linearly correlated with log *S*. The correlation coefficient exceeds 0.9 for all tested soils.

The above findings provide the basis to develop the model for the *λ *of Bavarian soils:

For 0 < *S* < *S*_{p}, *λ* = *λ*_{dry}.

For *S*_{p} < *S* < 1, *λ* = *λ*_{dry} + (*λ*_{sat} – *λ*_{dry}) * (1 – log *S* / log *S*_{p}),

where *λ*_{sat} is the *λ *value at saturated conditions. Using the physical properties, the multiple regression analysis derives the equations for *λ*_{dry}, *λ*_{sat} and *S*_{p}:

*λ*_{dry} = 0.30 * *r*_{d} – 0.21,

*λ*_{sat} = (7.7^{V}^{q} * 2^{(1-Vq)})^{V}^{s} * 0.6^{(1-Vs)}, and

*S _{p}* = 0.10 *

*m*

_{clay}*

*r*

_{d}+ 0.08,

where *r*_{d }is the bulk density, *V*_{q} is the volumetric quartz content expressed by “0.14 * m_{sand} – 0.67 * m_{clay} + 0.57”, *V*_{s} is the volumetric solid content expressed by “*r*_{d}/2.67” and *m*_{clay} is the clay content.

Figure 1 shows the measured and calculated *λ *values for different soil textures.* *The statistical analysis reveals that, on the average for all tested soils, the *λ* estimates correspond to the *λ *measurements within the RMSE of 0.11 Wm^{-1}K^{-1}.

**Conclusion**

We have developed a new model that successfully fits to the *λ* measurements of 21 selected Bavarian soils. As a future work, further model validation based on a larger dataset will be performed. The validated model will be applied for predicting the *λ *values of soil units of the soil survey map of Bavaria 1:25.000 (ÜBK25) thus enabling it to be a management tool for optimized site specific layout of horizontal GHE. Data will be made available for users in the internet (www.bis.bayern.de).