Relationship Between Thermal Conductivity, Mineral Composition and Major Element Composition in Rocks from Central and South Germany

Abstract

Thermal conductivity is a decisive parameter in all geothermal applications. In addition to the influencing factors of density, saturation, porosity, temperature and pressure, it is, above all, the geochemical and mineralogical composition that determines the thermal conductivity in rocks and soils. This study focuses on selected rock samples from Southern and Central Germany regarding major element oxides and minerals as well as distributed thermal conductivity. We examined clastic and chemical sedimentary, as well as igneous and metamorphic rocks, ranging from the Paleozoic to Cenozoic age. Measurements were conducted by X-ray fluorescence analysis (XRF), X-ray diffraction (XRD) and optical scanning with a thermal conductivity scanner (TCS). The results show significant correlations between thermal and geochemical parameters. Chemical composition significantly impacts thermal conductivity. Higher quartz and SiO₂ contents generally lead to increased thermal conductivity, while aluminum silicates, common in clay minerals, correlate with lower conductivity. For carbonates, increased density or reduced porosity enhances conductivity. Structural differences and differing mineral concentrations influence the measurement variability along the sampling axis. This is especially visible in clastic sedimentary rock samples, where porosity decreases while cementation of the matrix increases thermal conductivity.

1. Introduction

Knowledge of the thermal conductivity of the subsurface is the key to successful planning and implementation of shallow low enthalpy geothermal systems. Especially in the case of vertical systems, e.g., (double)-U-/coaxial-borehole heat exchangers or energy piles, knowledge of the bedrock is very important. In the case of a simple and homogeneous lithology, the thermal parameters are determined during planning by means of a thermal response test [1,2,3]. An effective thermal conductivity is measured over the entire borehole using a thermal input. In the case of more complex lithologies, it is necessary to examine the subsurface more thoroughly. In practice, depth-resolved tests, e.g., enhanced thermal response tests [4], data logger inspections [5] and core drillings, can be carried out for this purpose. The latter provides a more precise overview of the rock and allows measurements of the thermal properties. These properties are controlled by a variety of petrological, pedological and hydrogeological parameters. Various studies have been made on different materials, including rocks [6,7,8,9,10,11,12], soils [13,14,15] and single minerals [16,17], by using the steady-state or transient method with a variety of measurement instruments, e.g., divided bar [18,19], needle probe [20], thermal cell or guarded parallel/hot plate. In this study, we used an optical high-resolution scanning device, the thermal conductivity scanner (TCS), for measuring sampled rocks occurring in Central and South Germany. The method allows a nondestructive measurement, records the spatial distribution of the thermal conductivity in heterogeneous materials and has no strict requirements. Further studies showed that the TCS method yields consistent results compared to the divided-bar and line-source methods [21]. Subsequently we analyzed the rock samples regarding major element composition and rock-forming minerals and compared this with the thermal conductivity.

The thermal conductivity of rocks is largely determined by the mineral composition, the porosity (ϕ), and, in particular, the total porosity and the degree of saturation (S_r) [22,23]. Depending on the input parameters, different model approaches, either empirical models with input mineralogy [20], porosity [24], p-wave velocities [25] or estimation models based on machine learning [26,27], exist for a variety of rock types. New machine learning models can predict the thermal conductivity of plutonic rocks within a RMSE of 5% using the five main element oxides [26]. In this work, we tried to bring the newly gained data of Germanic rocks into the context of already existing thermal conductivity and geochemical models.

2. Materials and Methods

In order to record different lithological types, a selection of sediments, igneous and metamorphic rocks occurring in Central and Southern Germany (Bavaria, Hesse, Thuringia and Saxony) was chosen for further investigation with regard to their thermal properties, especially thermal conductivity and geochemical composition. For this, three different analytical methods were used, including a thermal conductivity scanner, an X-ray fluorescence spectrometer and an X-ray diffractometer.

2.1. Lithology

The samples of Paleozoic origin are mostly drilled cores from different depth levels up to a depth of almost fifteen meters below ground level (b. g. l.). These samples were taken during preliminary exploration for high-voltage power cable construction. Mesozoic and Cenozoic rocks were sampled on representative outcrops. Lithographic and general information of each sample is listed in

Table 1. Main characteristics of each sample used in this study; sorting is in descending order of age. Note: b.g.l.—below ground level.

Sample Type	Sampling Depth [m b. g. l.]	Geological Period /System	Lithostratigraphic Information
Clay slate I	6.2–6.5	Ordovician	Phycodenschiefer-Formation oPS
Clay slate II	5.0–5.25	Ordovician	Phycodenschiefer-Formation oPS
Clay slate III	7.5–7.9	Ordovician	Phycodenschiefer-Formation oPS
Clay slate IV	12.7–12.9	Ordovician	Phycodenschiefer-Formation oPS
Granite	12.7–13.0	Devonian	Görkwitz-Formation doG
Greywacke II	7.0–8.0	Carboniferous	Ziegenrück-Formation cuZ
Greywacke II	14.4–14.8	Carboniferous	Ziegenrück-Formation cuZ
Greywacke III	5.2–5.5	Carboniferous	Ziegenrück-Formation cuZ
Claystone	8.65–8.8	Lower Triassic	Calvörde-Formation suC
Sandstone I	7.4–7.6	Lower Triassic	Bernburg-Formation suB
Sandstone II	3.0–5.0	Upper Triassic	Löwenstein-Formation kmB
Sandstone III	Outcrop	Middle Jurassic	Eisensandstein-Formation jmES
Fe-rich Sandstone	Outcrop	Middle Jurassic	Eisensandstein-Formation jmES
Dolomite	Outcrop	Upper Jurassic	Frankenalb-Formation wFr
Limestone	Outcrop	Upper Jurassic	Ebermannstadt-Formation wE
Basalt	Outcrop	Oligocene	Not applicable
Quartzite	4.6–7.3	Pleistocene *	Bench gravel

* Represents the sedimentary depositional area; actual origin and age were not determined.

. Figure 1 shows the location of each sample. Samples taken from the boreholes are perpendicular to the bedding. Each drilled core has a diameter of 90 mm.

2.2. Thermal Conductivity Measurements

The samples were pre-treated with black paint. The black color applied to the samples is necessary for the absorption of the infrared heat waves emitting from the heat source during the measurement [29]. Drying of the samples was done at 70 °C for at least 48 h. The samples were measured at least three times to test the reproducibility of the measurements. For the calibration of the measurements, three different ranges of thermal conductivity with two standards each were used. The ranges for the standards are as follows: 0.709–1.350 W/(m∙K), 1.350–5.940 W/(m∙K) and 5.940–13.300 W/(m∙K); see also

Table 2. Key data of the thermal conductivity scanner (TCS) and set of standards at GeoZentrum Nordbayern labs; TC: thermal conductivity, TD: thermal diffusivity.

Parameter	Range	Accuracy
Thermal conductivity	0.2–25 W/(m∙K)	±3%
Thermal diffusivity	0.6–3.0 ∙ 10−6 m2/s	±5%
Sample Dimensions	30–500 mm	1
Standard	TC/TD Value [W/(m∙K)]/[mm2/s]	Dimension [mm]
Technical glass	0.709/0.401	55 × 55 × 10
Quartz glass	1.350/0.850	60 × 60 × 20
Gabbro	2.370/1.020	60 × 50 × 28
Titanium alloy	5.94/2.685	73 × 62 × 34
Stainless steel	13.3/3.619	80 × 70 × 40

¹ Minimum sample size is decisive for the accuracy of the measurement.

. The measurements were done using the optical scanning method [21,30] on a thermal conductivity scanner (TCS) by Lippmann and Rauen GbR, Schaufling, Germany at the GeoZentrum Nordbayern Labs at Friedrich-Alexander-Universität Erlangen-Nürnberg, at room temperature (22 ± 2 °C). The key parameters of the TCS are shown in Table 2. The measurement setup is displayed schematically in Figure 2. Measurements were conducted in air-saturated (dry) and water-saturated states. The saturation of samples was done after DIN EN 13755 [31] under atmospheric pressure. The scanning line crosses the most representative areas of each sample and follows the X-axis (longitudinal axis), as indicated in Figure 2. Saturated and dry measurements were conducted along the same lines. Correction of curvature was done automatically by the TCS software v. 5.0.

2.3. Geochemical Sample Preparation

The samples were mostly fresh and not altered. To avoid contamination of the chemical data, the rocks were cut into cuboids of approximately 15 cm³ by using different stone-cutting saws at the GeoZentrum Nordbayern labs.

The rectangular cuboids used for geochemical analysis were cleaned in an ultrasonic bath filled with deionized water for 15 min and subsequently dried in a compartment drier for 48 h at 60 °C. Afterward, the samples were crushed by a hydraulic press and ground into a powder with an agate vibratory ring mill, type Retsch RS200. Every crushed sample was ground for 15 min at 700 rpm to a particle size of approx. < 30 μm. Powder aliquots were dried for 24 h at 105 °C for X-ray fluorescence (XRF) and 48 h at 60 °C for X-ray diffraction (XRD) analysis.

The powder of each XRF sample was weighed to 2 × 1.000 g for the magmatic samples and 1 × 0.500 g for the sedimentary and metamorphic samples. One part of the magmatic sample was heated in a muffle furnace to 1050 °C for 12 h to determine the loss-on-ignition (LOI) of each sample. The other part was mixed with 4.83 g of di-lithium tetraborate (Bi₄Li₂O₇) as a disintegration agent and one spatula of di-iodine pentoxide (I₂O₅) as flux. The sedimentary and metamorphic samples were mixed with 4.00 g of lithium metaborate (LiBO₂) and further processed out of the LOI process. The mixture was melted on a five-stage “Oxiflux” burner system to a maximum temperature of 1050 °C. For both procedures, the aim was to generate a homogenous glass bead of each sample.

2.4. Major Element Analytic

X-ray fluorescence spectroscopy (XRF) measurements were carried out on the glass by using a Spectro XEPOS X-ray fluorescence spectrometer at the GeoZentrum Nordbayern. Measurements were conducted in the energy-dispersive mode (EDS). The major elements have been detected in weight percent (wt.%) of their oxides (SiO₂, TiO₂, Al₂O₃, Fe₂O₃, MnO, MgO, CaO, Na₂O, K₂O and P₂O₅), while Fe₂O₃ comprises the total content of Fe²⁺ and Fe³⁺. In addition, selected trace elements (Ba, Cr, Ga, Nb, Ni, Pb, Rb, Sr, Th, V, Y, Zn and Zr) have been detected in parts per million (ppm) (see Appendix A 

Table A1. Trace element results from X-ray fluorescence spectroscopy (XRF) in parts per million (ppm).

Sample Type	Ba	Cr	Ga	Nb	Ni	Pb	Rb
Clay slate I	723	74.0	22.5	11.0	46.6	2.4	148
Clay slate II	689	96.8	24.6	14.1	57.5	9.2	173
Clay slate III	566	94.7	24.4	12.1	50.1	6.2	152
Clay slate IV	660	96.2	27.3	14.7	58.5	13.6	174
Granite	759	11.2	22.1	37.5	6.9	5.6	112
Greywacke I	231	99.8	15.4	4.4	67.1	7.6	45.9
Greywacke II	318	96.4	15.0	5.6	48.4	7.1	58.5
Greywacke III	287	40.5	7.8	3.0	23.6	6.0	39.0
Claystone	260	97.9	13.2	5.1	61.8	3.9	57.3
Sandstone I	842	23.6	9.5	0.9	25.6	15.6	114
Sandstone II	576	19.5	8.3	2.1	11.4	14.1	86.8
Sandstone III	106	32.1	4.0	3.4	13.5	10.3	14.1
Fe-rich Sandstone	102	99.3	8.8	7.6	57.4	7.1	12.7
Dolomite	20.8	22.8	2.0	<0.5	2.3	<1.0	<0.5
Limestone	29.3	29.2	3.9	1.0	<0.5	1.7	<0.5
Basalt	971	136	18.1	70.9	92.3	4.1	66.6
Quartzite	54.7	16.9	2.4	<0.5	13.2	19.0	<0.5
Sample type	Sr	Th	V	Y	Zn	Zr
Clay slate I	71.9	13.5	92.7	31.5	99.3	210
Clay slate II	109	20.3	97.0	29.8	118	175
Clay slate III	91.0	18.4	102	26.8	91.3	181
Clay slate IV	85.4	21.2	96.9	33.2	118	184
Granite	62.6	10.4	2.9	48.4	33.3	486
Greywacke I	52.5	5.5	75.5	15.8	61.2	120
Greywacke II	63.6	5.8	92.9	17.9	42.8	139
Greywacke III	262	4.3	31.7	6.6	29.9	65.8
Claystone	60.1	6.6	91.1	18.1	58.3	149
Sandstone I	89.5	4.2	15.4	5.9	17.6	63.6
Sandstone II	69.0	5.7	16.9	1.5	15.7	64.1
Sandstone III	23.0	5.1	32.0	7.0	98.0	60.0
Fe-rich Sandstone	536	6.0	136	19.8	39.3	330
Dolomite	47.8	1.3	16.5	2.7	18.4	5.8
Limestone	248	2.1	20.1	5.8	34.9	10.1
Basalt	976	6.7	222	22.7	84.2	283
Quartzite	3.9	<1.0	1.3	<0.5	10.7	4.3

) but will not be used for this subject. To ensure accuracy and precision, three international standards, basalt (BR) and two granites (AC-E, GA), were measured repeatedly. The limits of detection and quantification of the major elements are shown in

Table 3. Limit of detection (LOD) and limit of quantification (LOQ) for major elements from XRF analysis.

Element	LOD [ppm]	LOQ [ppm]	LOQ [%]
SiO2	10.7	21.1	0.00321
TiO2	3.3	9.9	0.00099
Al2O3	37.8	113.4	0.01134
Fe2O3	1.4	4.2	0.00042
MnO	1.3	3.9	0.00039
MgO	33.2	99.6	0.00996
CaO	14.0	42.0	0.0042
Na2O	134.8	404.4	0.04044
K2O	12.0	36.0	0.0036
P2O5	6.9	20.7	0.00207

, and the values of the trace elements are max. 1.8 ppm for Vanadium.

2.5. Mineral Phase Analytic

X-ray diffraction (XRD) measurements were conducted using dried powder with <30 μm grain size for the mineral assemblage in powder diagrams. For this purpose, a Siemens D5000 Theta-Theta-diffractometer with Cu K alpha radiation at 35 mA and 40 kV at an angle range of 2–65° 2θ with a stepscan of 0.02° was used. Qualitative and quantitative analyses were carried out using Rietveld analysis (RVA) [32,33].

2.6. Density and Porosity Measurements

The density was calculated by the volume and dry weight of the rectangular prisms. The porosity was measured by two methods using (a) the open porosity calculation by DIN EN 1936 [34] and (b) true density with a Micromeritics AccuPyc II 1345 gas pycnometer as well as (c) the porosity and bulk/envelope density with a Micromeritics GeoPyc 1365 envelope and density analyzer both by Micromeritics Instrument Corporation, Norcross, GA, USA. True density was measured for all samples, while Formula (1) was used for open porosity ϕ_O to provide a preliminary estimate.

$${\varphi }_O={\displaystyle \frac{m_s-m_d}{m_s-m_h}}\times 100$$

(1)

where m_s is the saturated weight, m_d is the dry weight, and m_h is the hydrated weight. Specifications of the AccuPyc gas pycnometer are as follows: volume accuracy of 0.02%, volume repeatability of 0.01%, temperature range from 4 °C to 60 °C and a temperature stability of ±0.025 °C. Specifications of the GeoPyc analyzer are reproducibility ±1.1% at a minimum sample size of 25% volume of the sample holder. Each sample was weighed, and the true density was measured via a helium gas pycnometer with 10 measurement cycles. Further processing for porosity measurements was performed by the addition of the Micromeritics “DryFlo” mixture of differing size particles and a small quantity of graphitic lubricant. Each measurement was repeated 10 times with a consolidation force of 145.00 N.

3. Results

We analyzed 17 representative rock samples from Central and South Germany. Investigations of the thermal conductivity and the element and mineral analytics are displayed in two subsections. The petrographic on-site examination and the geochemical composition of the samples are in concordance. The measured thermal conductivity values are within the range specified in VDI 4640 [35].

3.1. Thermal Conductivity via Thermal Conductivity Scanner (TCS)

The thermal conductivity ranges from average values of 1.19 W/(m∙K) for dry claystone to 6.85 W/(m∙K) for dry quartzite and 2.24 W/(m∙K) for saturated claystone to 8.06 W/(m∙K) for saturated quartzite. Rocks from other sedimentary origin show distinct higher values with λ_dry = 1.72–3.27 W/(m∙K) and λ_sat = 2.24–2.96 W/(m∙K) for sandstones and λ_dry = 2.85–3.91 W/(m∙K) and λ_sat = 2.35–3.07 W/(m∙K) for limestone and dolomite. Thermal conductivity on igneous rocks was measured between λ_dry = 1.91 W/(m∙K) and for λ_sat = 1.57 W/(m∙K) for basalt and λ_dry = 1.98 W/(m∙K) and λ_sat = 2.96 W/(m∙K) for granite. Paleozoic metamorphic rocks from Thuringia and Saxony show values of λ_dry = 1.39–1.79 W/(m∙K) and λ_sat = 2.44–2.96 W/(m∙K) for clay slates and distinctly higher values for greywackes ranging from λ_dry = 2.62–3.94 W/(m∙K) and λ_sat = 3.22–3.75 W/(m∙K).

Table 4. Mean values for thermal conductivity of each sample in dry and saturated conditions with the relative standard deviation (RSD = standard deviation/mean value) of each measurement and measured porosities and densities in dry conditions.

Sample Type	Thermal Conductivity λdry [W/(m∙K)]	RSD λdry [%]	Thermal Conductivity λsat [W/(m∙K)]	RSD λsat [%]	Porosity ϕ [%]	True Density ρ [g/cm3]	Bulk Density [g/cm3]
Clay slate I	1.79	8.9	2.44	4.3	14.78	2.77	2.36
Clay slate II	1.64	4.3	2.56	3.7	10.39	2.78	2.49
Clay slate III	1.39	7.9	2.64	7.0	9.79	2.78	2.51
Clay slate IV 1	1.40	7.5	2.43	7.6	8.63	2.80	2.56
Clay slate IV 2	1.69	12.4	2.96	12.1	8.63	2.80	2.56
Granite	1.98	6.6	2.96	5.3	0.69	2.66	2.62
Greywacke I	2.62	6.9	3.22	3.7	4.79	2.72	2.61
Greywacke II	3.94	4.5	3.75	4.5	2.50	2.69	2.63
Greywacke III	3.17	6.5	3.65	3.3	3.50	2.71	2.62
Clay stone	1.19	8.2	2.24	8.9	16.16	2.63	2.39
Sandstone I	1.72	3.5	2.94	3.6	17.48	2.65	2.18
Sandstone II	3.27	6.7	2.96	5.1	12.9	2.64	2.30
Sandstone III	2.21	8.2	2.83	7.1	28.94	2.70	1.91
Fe-rich Sandstone	1.96	9.4	2.42	5.2	19.51	2.92	2.25
Dolomite	3.91	5.6	3.07	6.2	5.93	2.81	2.64
Limestone	2.85	4.7	2.35	5.1	27.3	2.71	1.97
Basalt	1.84	4.3	1.57	2.1	<0.1	2.90	2.94 3
Quartzite	6.85	13.6	8.06	20.7	<0.1	2.63	2.69 3

¹ Measurement parallel to the slate surface; ² measurement orthogonal to the slate surface. ³ measurement errors due to very low porosity.

shows the thermal conductivity values for each sample as well as the relative standard deviations. Figure 3 depicts the length-resolved measurements of each sample in categories of similar rock types. True density and bulk density were measured via a pycnometer. These ranged from 2.63 to 2.92 g/cm³ (ρ_True) and 1.92 to 2.94 g/cm³ (ρ_Bulk). Total porosity ranged from <0.1 to 28.94% (see Table 4). The standard deviations of the density measurements show low deviations, with the highest value of 0.101 g/cm³ and a mean value of 0.008 g/cm³.

3.2. Major Element and Mineral Phase Analytic

The major element analytic by XRF provides quantitative results in a weight percent of their oxides. All values can be found in

Table 5. Major element oxide results from X-ray fluorescence spectroscopy (XRF) in weight percent (wt.%) and the loss-on-ignition (LOI) for each sample. Trace element values are in Appendix A Table A1.

Sample Type	SiO2	TiO2	Al2O3	Fe2O3	MgO	CaO	Na2O	K2O	LOI
Clay slate I	66.1	0.82	17.76	5.58	1.48	0.11	0.66	3.39	3.70
Clay slate II	60.4	1.0	20.89	6.58	1.62	0.11	1.14	3.78	4.19
Clay slate III	65.3	0.91	18.60	5.34	1.31	0.08	1.32	3.47	3.30
Clay slate IV	60.6	0.96	20.71	6.72	1.62	0.06	1.24	3.74	3.88
Granite	75.7	0.39	13.10	1.34	0.19	0.10	3.32	3.91	1.65
Greywacke I	73.3	0.52	10.51	4.78	2.23	1.17	2.19	1.16	3.73
Greywacke II	73.7	0.59	11.80	3.71	1.66	0.511	2.59	1.71	3.22
Greywacke III	83.0	0.18	4.07	0.99	0.33	6.52	0.79	1.14	2.52
Clay stone	73.7	0.59	11.16	3.92	1.27	0.225	2.36	1.50	4.87
Sandstone I	73.0	0.09	7.84	0.54	3.03	3.61	0.55	4.50	6.45
Sandstone II	88.7	0.12	5.92	0.33	0.084	0.04	0.61	2.80	1.18
Sandstone III	93.2	0.18	1.35	2.59	0.066	0.07	0.55	0.56	1.22
Fe-rich Sandstone	69.7	0.39	4.52	19.05	0.351	0.06	0.54	0.49	4.20
Dolomite	0.3	0.03	0.81	0.25	20.79	31.10	0.11	0.01	46.43
Limestone	1.4	0.04	0.39	0.34	1.11	53.52	<0.01	0.02	42.89
Basalt	45.1	2.56	15.80	9.56	7.73	10.01	3.31	2.10	2.50
Quartzite	99.3	0.22	<0.01	0.11	<0.01	0.01	0.33	0.01	0.22

. The metamorphic rocks’ range shows moderate values of 60.6 to 66.1 wt.% SiO₂, high values of 17.8 to 20.9 wt.% Al₂O₃ and 5.3 to 6.7 wt.% Fe₂O₃, with the exception of the Quartzite sample. Clastic sediments are represented by high values of 69.7 to 93.2 wt.% SiO₂, moderate to low values of 1.35 to 11.8 wt.% Al₂O₃ and low values of 0.99 to 4.78 wt.% Fe₂O₃, with the exception of “Eisensandstein Fm” sandstone with 19.05 wt.% Fe₂O₃. The carbonate sedimentary samples show typical high values of 31.1 wt.% and 53.5 wt.% CaO and high loss-on-ignition (LOI) for dolomite and limestone and additionally a high value of 20.8 wt.% MgO for dolomite. Igneous rocks show characteristic values, as shown in Table 4. Values for MnO and P₂O₅ are for all samples underneath 0.1 wt.% and 0.7 wt.%, respectively, and are therefore not listed in the table.

Measurements of mineral phases via XRD show values for the main rock-forming minerals. An exact quantity for each mineral and the XRD patterns can be found in

Table A2. Percentage of mineral phases in each sample measured with XRD.

Clay Slate I		Clay Slate II		Clay Slate II		Clay Slate II
Quartz	50.2	Quartz	35.9	Quartz	42.6	Quartz	38.3
Muscovite	37.1	Muscovite	43.1	Muscovite	38.2	Muscovite	40.7
Chlorite	11.9	Chlorite	14.1	Chlorite	11.1	Chlorite	15.2
K-Feldspar	0.7	Plagioclase	3.6	Plagioclase	6.8	Plagioclase	3.7
		K-Feldspar	3.1	K-Feldspar	1.1	K-Feldspar	1.9
Granite		Greywacke I		Greywacke II		Greywacke III
Quartz	42	Quartz	55.3	Quartz	54.6	Quartz	56.4
Muscovite	7.1	Muscovite	8.3	Muscovite	16.8	Muscovite	19.1
Chlorite	1.7	Chlorite	13.2	Chlorite	7.8	Chlorite	7.2
Plagioclase	27.5	Plagioclase	19.2	Plagioclase	19.9	Plagioclase	17.2
K-Feldspar	21.5	K-Feldspar	1	K-Feldspar	0.6
		Dolomite	2.8
Sandstone I		Sandstone II		Sandstone III		Fe-rich Sandstone
Quartz	56.3	Quartz	74	Quartz	89	Quartz	55
Muscovite	3.8	K-Feldspar	14	Goethite	11	Goethite	38
K-Feldspar	28.5	Illite	6			Hematite	7
Dolomite	11.3	Kaolinite	6
Claystone		Basalt		Quartzite
Quartz	24	Chlorite	5	Quartz	100
Muscovite	9	Plagioclase	36	Dolomite
Chlorite	4	Diopside	33	Dolomite	100
K-Feldspar	10	Natrolite	4	Limestone
Hematite	3	Analcime	8	Quartz	1
Illite	50	Leucite	2	Calcite	99
		Nepheline	5
		Forsterite	7

and Figure A1 (Appendix A). Clay slates, greywackes and sandstones have medium to high values of quartz, with 35.9% to 50.2% in clay slates, 54.6% to 56.4% in greywackes and 55.0% to 89.0% in sandstones. Clay slates commonly have high percentages of mica (muscovite) and clay minerals (illite, chlorite). Greywackes have medium values of plagioclase 18.8 ± 1% as well as fluctuating contents of muscovite and chlorite, ranging from 8.3% to 19.1% and 7.8% to 13.2%, respectively. Granite and basalt samples show common values for rock-forming minerals quartz, plagioclase and potassium, as well as pyroxene, plagioclase and olivine (see also Table A2 and Section 4.2).

4. Discussion

4.1. Contributing Factors Not Measurable in Laboratory Scale

As shown in previous studies, the thermal conductivity of the subsoil is subject to many factors, such as grain size, porosity, pressure, temperature, degree of saturation or matrix composition [7,36,37]. This study focuses on rocks in shallow areas. The rock-forming parameters, temperature and pressure were not investigated in this study since they are not applicable in shallow depths. Depending on the location, the geothermal gradient is first visible at depths of approx. 100 m or more [5]. Nevertheless, temperature has a great influence on thermal conductivity and diffusivity [38]. In the applied use of shallow geothermal energy, the hydrogeological surrounding of the system has a big influence on the effectiveness [39,40,41,42,43]. In this case, the thermal properties can be measured more accurately by using depth-resolved solutions, e.g., distributed temperature sensing [5] or the implementation of the moving infinite line source for calculating thermal conductivity during thermal response tests [1,44]. Porosity and density are the main parameters that have a great influence on thermal conductivity [45]. In situ measurements, such as eGRT or TRT [4,5,46], of thermal properties can show depth-resolved values for thermal conductivity and heat capacity but do not consider petrophysical parameters.

4.2. Classification of Samples

The sampled greywackes show common geochemical values. By using the logarithmic relationships between SiO₂/Al₂O₃ and Na₂O/K₂O [47,48,49], samples greywacke I + II are classified as greywacke while sample greywacke III is, in fact, bordering on being arkose. The density and thermal conductivity of greywackes are similar to samples from other studies, e.g., [50,51]. Sandstone I + II and Fe-rich sandstone are arkoses and a subarkose, respectively, while sandstone III is quartz arenite. Following the classification of log (Fe₂O₃/K₂O), sandstone III and Fe-rich sandstone are iron sandstones. Lithofacies classification of mudstones [52,53] categorizes the claystone sample as clay-rich siliceous mudstone. Following the classification of total alkali vs. silica (TAS) for major element oxides [54], the sampled basalt is on the border between basalt and basanite. This is common for the sampling area Rhön, Northern Bavaria (see Figure 1) [55]. TAS for plutonic rocks [56] classifies the sampled granite as just that. The slate samples are representative of major elements content with a focus on SiO₂, Al₂O₃ and Fe₂O₃ when compared to other studies [57,58]. The quartzite sample is mainly used as a reference for high SiO₂ content at high thermal conductivity.

All in all, all samples are representative in terms of their geochemical composition. In terms of thermal conductivity, the range of measured values is significantly greater and often highly heterogeneous depending on the microstructural composition. This is particularly the case with sedimentary and metamorphic rocks. The λ-values for the sampled rocks are located in a range of generally applicable literature, such as VDI 4640-1 [35], and can be found in other studies [27,59,60].

4.3. Combination of Geochemical and Geothermal Properties

The chemical composition has a decisive influence on thermal conductivity. Figure 4a,b show the thermal conductivity in relation to the SiO₂ and quartz contents. This shows the much-described trend of increasing thermal conductivity with increasing quartz content, as well as SiO₂ [7,61,62], with the exception of carbonate rocks. Rocks with a high proportion of aluminum silicates, which are frequently found in clay minerals, have a lower thermal conductivity. The ratio of Al₂O₃ to SiO₂ is the highest in metamorphic slates and claystone, which have the lowest thermal conductivity, also visible in Figure 4c. Bulk density and true density show diverging values when compared with the thermal conductivity; porosity ranges up to approx. 29% without any significant correlations visible (Figure 4f–h). Values of ρ_true provide a better understanding of the mineral and grain densities. The influence of CaO (Figure 4d) is not visible from the data in this study.

An important factor that must be considered is the measurement concept. The optical scanning method is well-established and delivers reliable data on thermal conductivity [27,30,63]. As this method produces heterogeneous, distributed data along a sample, interpretation must be done carefully. Our results show deviations along the measurement axis, as visible in Figure 2. These deviations are caused, on the one hand, by different minerals and mineral accumulations, e.g., in shales, and on the other hand, by porosities or different measuring distances of the sample, as seen in the results of the quartzite sample (Figure 3e). Previous studies have investigated the significant deviations caused by inhomogeneities in the rocks and developed various approaches [45,64]. These include thermal conductivity and the porosity maps method, which allow a more detailed insight into the thermal conductivity distribution. This comprises porosity, on the one hand, and mineral accumulations from sedimentary or metamorphic arrangement, on the other. The deviation due to mineral arrangement is visible in the clay-slate measurements, especially during orthogonal orientation, but also in certain cases of sedimentary rocks, e.g., sandstone II. In this case, the XRD measurements indicate that the larger fluctuations are caused by matrix-forming potassium feldspar (14%). This can be repeatedly observed in all three greywacke samples. Different orders of magnitude in measurement deviation are potentially driven by the mineralogical content. The basalt and greywacke samples clearly show that the SiO₂ content alone is not a direct indication of an increase in thermal conductivity.

4.4. Influence of Porosity and Density

The pore volume or porosity and density of materials have a great influence on thermal properties. Thermal conductivity of bodies with random porosity, as in the case of most rocks, is decreased proportionally to the volume pore fraction [65]. Porosity is related to the internal rock structure and geometry while processes after rock forming can also have a great impact [66]. In the case of the samples in this study, the factor of alteration must be considered since the samples are all from very shallow drillings and outcrops. Furthermore, sedimentary samples and potentially hydrothermal altered samples, such as the metamorphic clay slates, are subject to different forms of intergranular cementation [36,37,66]. Porosity favors possible saturation and can thus contribute to an increase in thermal conductivity. We observed that the Mesozoic sandstones and Paleozoic greywackes show relatively low values of thermal conductivity with increasing porosity (see Figure 5). In the case of these sediments, this correlation appears to be due to the low amount of pore volume or, conversely, the high proportion of cementation or matrix. This can, therefore, also be transferred to the noticeably more compact and finer graywackes. While the true density and bulk density of clay slates are relatively high due to metamorphic overprinting, porosity is more distinctive with the siliciclastic samples.

4.5. Comparison with Prior Studies

Measurements of thermal conductivity via TCS are a common procedure [21,23,30,64]. This promotes a good comparability of measurements, even though each rock type has a wide range. The saturation method creates deviations, e.g., by use of Ar-gas or oil [12]; therefore, only water-saturated and dry samples are listed in Table 5. As already mentioned, all thermal conductivity values are within the ranges specified in VDI 4640 [35]. The values for the thermal conductivity of sandstone have a great variability in comparison to rock samples [23] from Northern Bavaria, which show significantly higher values. Igneous rocks are within the range of measured samples from other studies [9,10]. The carbonatic samples match similar rock types of fine mudstone. Overall thermal conductivity matches with world-wide published values. An overview of publications with comparable values is shown in

Table 6. Related work with similar lithological investigations. Note: TC: thermal conductivity; suBB: Bernburg-Fm, “Basissandstein”; suBT: Bernburg-Fm, “Tonlagensandststein”.

Previous Studies	Sample Type	TC [W/(m∙K)]	Further Investigations	TC (This Work) [W/(m∙K)]
Franz & Schulze (2016) [23]	Sandstones suBB	λdry: 2.91 ± 0.31 λsat: 3.96 ± 0.37	Quarzitic cementation	λdry: 2.78 ± 0.36 λsat: 2.29 ± 0.37
	Sandstones suBT	λdry: 2.54 ± 0.35 λsat: 3.85 ± 0.38	Inter-bedded claystone
Barry-Macaulay et al. (2013) [9]	Basalts	λdry: 0.56–1.05 λsat: 1.08–1.57	ρ = 1.75–2.61 g/cm3	λdry: 1.84 λsat: 1.57
Landesamt für Geologie und Bergbau Rheinland-Pfalz [67]	Clay slates	λdry: 1.27–3.45 λsat: 2.09–3.63	Devonian clay slates	λdry: 1.40–1.79 λsat: 2.43–2.96
	Arkose	λdry: 1.44–2.00 λsat: 1.93–2.57	Carboniferous (Rotliegend) arkose	λdry: 2.62–3.75 λsat: 3.22–3.94
Long et al. (2017) [10]	Limestones	1.12–1.85	Varying TC range depending on mudstone percentage	λdry: 2.85–3.91 λsat: 2.35–3.07
	Muddy limestones	1.97–3.70
	Sandstone	1.40–4.38	Depending on clay/mud/calcareous cementation	λdry: 2.78 ± 0.36 λsat: 2.29 ± 0.37
	Granites (+rhyolite)	1.4–3.07		λdry: 2.96 λsat: 1.98

.

5. Conclusions

In this study, a set of 17 rock samples from the Paleozoic to Cenozoic age was analyzed regarding their geochemical compositions via XRF and XRD and thermal conductivity via TCS. The samples ranged from clastic and chemical sedimentary rocks, namely sandstones, greywackes, claystone and carbonates, to igneous and metamorphic rocks, and more precisely, basalt, granite, quartzite and clay shales. The results of the investigations are in concordance with previous studies. Our further conclusions are as follows:

• A new dataset of geochemical and thermal properties of rocks from Central Germany was created. The rocks were selected to cover the main areas of central German geology.
• The resulting thermal conductivity values are in a range between 1.19 and 6.85 W/(m∙K) in a dry state and 2.24 and 8.06 W/(m∙K) in a water-saturated state.
• The chemical composition significantly impacts thermal properties, especially a high quartz content rather than SiO₂ content, and increases thermal conductivity in SiO₂-bearing rocks. Aluminum silicates, occurring in slates and clay stone, correlate with lower thermal conductivity. Rock density correlates partly with thermal conductivity.
• Heterogeneities due to mineral concentrations and structural differences can be well displayed and analyzed with TCS.

In order to analyze the main influencing parameters further, especially upon closer examination of the mineral phases and accumulations and sedimentary cementations, the next step in this research is the use of scanning electron microscopy (SEM). In this way, grain size, grain connection and the porosity effects can be examined in more detail. This can be further supported by 2D mapping of selected heterogeneous rocks regarding thermal conductivity and porosity, e.g., as conducted by [45,64].