Evaluation of Thermal Performance of Ground - Source Energy Systems. A Geophysics Supported Approach

Georgios Fragogiannis1, Nikolaos Papatheodorou1 and Prof. Sofia Stamataki 1 1 National Technical University of Athens, School of Mining Engineering and Metallurgy, GREECE. Tel: 30 210 772 2202, Fax: 30 210 772 2203, Email: stamat@metal.ntua.gr 1. Introduction Utilization of ground as a heat source has been proved a very promising technology for several applications in residential, commercial and agricultural sectors. Ground-source heat pump (GSHP) systems have extensively grown in Europe and U. S. A. in recent two decades and appear significant advances since energy saving and environmental protection becomes one of the major interest of modern societies. The design of a ground heat exchanger for GSHP systems requires, at a minimum, the knowledge of the thermal properties of the ground, in particular, of the thermal conductivity. In the case of vertical borehole heat exchangers (BHE) these properties vary with depth and are strongly dependent on the geology and hydrogeology of the subsurface environment. Common practice for determining thermal conductivity of soils is the use of generalized empirical correlations based on the type and composition of the soil as well as the state of compaction (i.e. density, moisture content) (Bristow, 1998). The efficiency of these relationships depends on the range of the experimental data they have been developed on and unacceptable high errors are often observed (Tarnewski, 2000). An additional tool is the in situ measurement by applying a thermal response test (TRT) in a ready-to-operate BHE (Sanner, 2007). The evaluation of the recorded temperatures versus time provides an estimation of the average thermal conductivity in the vicinity of the BHE. The accuracy of the TRT depends largely on the length of experiment and the optimum duration is still an on-going debate mainly because longer tests entail greater expenses. On the other hand, TRT measurement is a local value and it may prove dangerous to use it as a site representative figure, especially in areas of complex geology. Both methodologies have been applied to a site at the Campus of National Technical University

of Athens (Greece) where a GSHP system of 12 vertical borehole heat exchangers is installed. The main achievement of this work is the combined use of electrical resistivity geophysical methods to obtain a detailed image of the subsurface and to construct electrical resistivity sections through the underlying structures. An effort has been made to the interrelation of electrical resistivity values to the thermal conductivity ones and to generate thermal conductivity profiles for each section. 2.Site geology - Geotechnical characterization The geology of the wider area is characterized by alluvial deposits overlaying clay and carbonate schist. Underneath, consolidated limestone is met. According to the quantitative observations from borehole drilling during the installation of the GSHP system (project technical report, 2000), the local geology is estimated as follows: 1. 0-5 m: surface alluvials. 2. 5-45 m: loose marble conglomerates with

minor amount of silt and clay (recent scree). They can be classified as sand and sandy loam soil type.

3. 45-95 m: schist with thin marble intercalations.

Considering that during drilling no systematic sample analysis took place, the above estimation is under consideration. Moreover, there is no available data for subsurface parameters (moisture content, density, saturation, particle size fraction of soil etc) which are critical to the design of such type of systems. For the determination of all required information the following steps were executed in a combined approach: a. Soil sampling and grain size analysis from

the area under investigation (site 1). b. Geophysical survey by applying electrical

resistivity tomography to site 2, vicinage to site 1. Interpretation of geophysical data in relation to all other type data available for this region, (site 2).

c. Application of electrical resistivity tomography on site 1. Interpretation of geophysical data, taking into account the findings of step 2 as well.

2.1. Soil sampling and texture Soil samples from 6 different positions from site 1 were collected and analyzed. The AASTHO (American Association of State Highway and Transportation Officials) soil classification system has been followed. According to this system particle size grading is: clay

Table 2. Geological model and formation characteristics of site 1

*mean electric resistivity [.m] of the area (based on the results of site 2) and the expected configuration of a riverbed up to a depth of 40 m. Through an integrated analysis, correlation and processing of all the aforementioned information, the resultant geological model for site 1 and the characteristics of the soil type layers met in this specific area are estimated as shown in Table 2. 3. Prediction of thermal conductivity Based on the model of site 1 as it is presented on Table 2, the evaluation of the thermal conductivity has been performed on the basis of four different approaches: 3.1. ASHRAE and Earth Energy Designer (EED) recommended values. Tabulated thermal conductivity values provided from ASHRAE for several soil and rock type formations (ASHRAE Applications, Handbook 1999, Kavanaugh, Rafferty, 1997) as well as those from EED have been used for the prediction of the weighted, in terms of formation thickness, average thermal conductivity (effective conductivity) of site 1. Table 3 presents the recommended min, mean and max values for each soil and rock type formation met in our case and the resulting effective thermal conductivity. The values derived from ASHRAE correspond to heavy sand soil type (Pd=1.925 gr/cm3 and w=5%), while for the later soil layer (sandy loam) a value of w=15% is used. EED values correspond to moist sand soil. The wide variation of the resulting values from each method will turn to unequal design parameters (such as the length of BHE), since the ground heat storage is differently estimated.

Table 3. Thermal conductivity predictions through ASHRAE and EED recommended values.

Thermal Conductivity (W/m.K) EED ASHRAE Depth

[m] Soil/Rock

type mean min max mean min max

0-8 Coarse Sand (moist) 1 0.58 1.75 2.2 2.1 2.3

8-25 Sand - loam sand (moist) 1 0.58 1.75 2.2 2.1 2.3

25-45 Sandy loam (moist) 1 0.58 1.75 3.3 2.8 3.8

45 - 95 Schist 2.1 1.50 2.6 1.9 1.4 2.4Effective thermal

conductivity 1.58 1.06 2.2 2.27 1.88 2.67

3.2 The use of empirical correlations For the estimation of soil thermal conductivity various generalized relationships have been developed. One group assumes that soil is a three phase medium (solid, liquid and air) and thermal conductivity is dependent on the ratio of these phases. The correlations of De Vries (1962), Johansen (1975), Singh (1995), and Tarnawski (2000) belong to this group. The second category is based on experimental data and best fit methods. Such correlations that can be applied to the type of soil present on site 1 are those of Kersten (1949), Campbell (1985), Singh (2000) and Shang (2007). For the correlations of group one it is assumed that the temperature of the subsurface soil is 20 oC and the thermal conductivity of each phase in the soil is according to De Vries (1963) and Kimball (1976) as, ks=2.93 W/m.K, kw=0.552 W/m.K and ka=0.0237 W/m.K.

Depth Soil texture % Formation properties

[m] Geological strata Soil type Electric

resistivity [.m]

Gravel Sand Silt - Clay Gs Pd

[gr/cm3] w

[%] Sr

[%]

0-8 Coarse Sand >200 (350)* 54.8 39.5 5.7 2.75 1.72 6 28

8-25 Sand - Loam sand

75-200 (120)*

65 52

23 38

12 10 2.72 1.79 8 42

25-45 Sandy loam

The aforementioned relations have been applied to each soil layer of site 1. For the case of schist where no data is available, therefore, correlations can not be used, the recommended by ASHRAE max thermal conductivity value (consolidated schist, k=2.4 W/m.K) is utilized. Table 4 presents the results coming from the first group of correlations, while Table 5 illustrates the results from the second one. All correlations behave consistently in terms of the variation of thermal conductivity prediction with depth. The results of Tables 4 and 5 indicate a substantial deviation between the different relationships. Those of Singh (1995), De Vries and Campbell, although they follow different approaches in tackling the problem, come to similar predictions. The same is valid for the correlations of Johansen and Kersten but they provide lower prediction values. The results from Singh (2000) and Shang are substantially higher.

Table 4.Predictions by correlations of group 1

Calculated thermal conductivity

[W/m.K]

depth [m] De

Vries Singh (1995) Johansen Tarnewski

0-8 1.245 1.277 0.805 0.560 8- 25 1.390 1.379 0.975 0.793 25-45 1.492 1.463 1.438 1.322 45- 95 2.40 2.40 2.40 2.40

effective value 1.93 1.93 1.81 1.73

Table 5. Predictions by correlations of group 2

Calculated thermal conductivity

[W/m.K]

depth [m] Kersten Cambell Singh (2000) Shang

0- 8 0.855 1.271 1.852 2.0748 - 25 1.158 1.379 2.184 2.52425- 45 1.433 1.504 1.650 2.78545- 95 2.40 2.40 2.40 2.40

effective 1.84 1.93 2.16 2.48 3.3 Thermal response test (TRT) TRT is a well established method to determine design parameters for borehole heat exchanger systems: borehole thermal resistance and effective ground thermal conductivity. The basis of the TRT methodology is the application of a constant energy flux to the ground and the

acquisition of the fluid temperature response over time. The analysis of the response test data is based on a description of the heat as being injected from a line source (Mogensen 1983, Eskilson 1987, Hellstrom 1991). The transient process that starts when heat is injected into a borehole is approximated by:

2

1 4ln( ) ln 4 4f b surb

Q QT t R TkH H k r

= + + +

(1)

If Q/H is constant, the last two terms do not change with time and Eq. (1) is simplified to:

ln( )fT t m= + (2) where and m are constants. is proportional to the thermal conductivity according to Eq.(3).

4Qk

H= (3) TRT was performed on site 1 in a vertical borehole of 95 m equipped by a double U-tube type collector and backfilled with bentonite. Constant heat (Q=5.562 KW) was being injected into the BHE for two days and the inlet and outlet fluid temperature was recorded over time. The thermal conductivity is estimated by plotting the mean fluid temperature versus time and match the plot of the experimental mean fluid temperature with curves for different thermal resistances according to Eq. (1). Once the thermal conductivity is graphically estimated from the inclination of the curve, Eq. (3), the thermal resistance comes out of the temperature level of the fluid.

Evaluation period

20

22

24

26

28

30

32

34

6 7 8 9 10 11 12lnt

Tem

pera

ture

(Cel

sius)

Tf - Theoritical k=2.1W/m.K, Rb=0.1 m.K/W

Tf - Experimental

Figure 3. Mean fluid temperature from response test at site 1, fitted to Eq. (1) with k=2.1 W/m.K and Rb=0.1 m.K/W Figure 3 illustrates the TRT results at site 1 following the above method. The effective thermal conductivity is predicted as k=2.1 W/m.K and the borehole thermal resistance as

Rb=0.1 m.K/W. This graphical method allows an accuracy of k0.05 W/m.K and Rb0.005 m.K/W. The value that comes out for the effective thermal conductivity is close to those of EED (max) and ASHRAE (mean) and in agreement to the prediction of Singh (2000). 3.4. A geophysics supported approach Figure 1 represents the interpretation of the ERT performed on site 1. Soil electrical resistivity is a measure of the resistance offered by the soil against passage of current through it whereas soil thermal resistivity is a measure of the resistance offered by the soil to the passage of heat. The experimental work of Singh et al (2001) indicated that the variation of electrical and thermal resistivity of soil with moulding degree of saturation is similar; therefore, the two resistivities can be correlated. The proposed generalized relationship is:

log R log RE R TC= (4)The multiplier parameter CR can be obtained from Eq.( 5 ),

1.34 0.0085RC F= + (5)where F (%), is the sum of the gravel and sand size fractions in the soil. The experimental work of Sreedeep et al (2005) extended Eq.(6) to the saturation of soil by the following generalized expression:

Sr ZRC X Y e

= + (6)where X, Y and Z are constant parameters, they depend mainly on the soil type and can be represented as:

(7) (8)

/ 25

1.1 0.010.9 0.010.02 0.0006 F

X FY FZ e

= + = = +

(9)

Both methodologies of Singh et al (2001) and Sreedeep et al (2005) have been utilized in this work. The soil electrical resistivity values have been translated to thermal resistivity ones using either Eq.(4) and (5), or Eq. (6) to (9) accounting saturation as well. The parameters F and Sr assumed to vary with depth following a continuous function derived from data of Table 1. Since thermal resistivity is predicted, the thermal conductivity is also known by k=1/RT. Figure 4 presents the generated thermal conductivity profiles at the site under investigation (site 1). In case [b] thermal resistivity has been evaluated considering soil saturation.

-20 -15 -10 -5 0 5 10 15 20

-35

-30

-25

-20

-15

-10

-5

0

0.30.50.70.91.11.31.5

-20 -15 -10 -5 0 5 10 15 20

-35

-30

-25

-20

-15

-10

-5

0

[a]

[b]

k [W/m.K]

[1] [2]

Figure 4. Distribution of thermal conductivity values in the subsurface of site 1. [a]: thermal resistivity estimated from eq. 5. [b]: thermal resistivity estimated from eq. 6-9. Figure 5 illustrates the thermal conductivity that can be derived thought this approach at two different locations of site 1. Location [1] refers to the place where TRT has been performed, while location [2] is at a distance of 23 m. There is a visible variation between the locations as well as between the prediction performance of the two approaches: Singh (2001) (k[1] and k[2]) and Sreedeep (2005) (k[1] and k[2]). Table 6 presents the estimated effective thermal conductivity at each location. At location [1] the resulting effective value is in a very good agreement to that from TRT and substantiates the efficiency of the method. At location [2], as expected due to the variations of Figure 4, an effective thermal conductivity of different value comes out. The incorporation of soil saturation leads to lower estimations with more pronounced deviations as saturation increases.

-45

-40

-35

-30

-25

-20

-15

-10

-5

00,4 0,6 0,8 1 1,2 1,4 1,6 1,8 2 2,2

Thermal conductivity (W/m.K)D

epth

(m)

Figure 5. Thermal conductivity versus depth at two different locations [1], [2] of site 1. Table 6. Effective thermal conductivity at locations [1] and [2] of site 1.

Estimated thermal conductivity [W/m.K] depth [m] k[1] k[1] k[2] k[2]

0-8 0.90 0.69 0.95 0,73 8-25 1.41 1.13 1.20 0.95

25-45 2.00 1.55 1.49 1.17 schist 2.40 2.40 2.40 2.40

effective value 2.01 1.85 1.87 1.74

4. Conclusions The combined study presented in this work serve to a better understanding of the effectiveness and limitations of the common methods that can be used for the estimation of the ground thermal conductivity. The proposed geophysical technique found quite efficient to provide a global quantitative distribution of thermal conductivity in the entire area of interest. Electrical resistivity tomography sections can be effectively translated to thermal resistivity profiles accounting not only the inner geological strata but also the lateral and vertical inhomogeneities as well as the hydrological conditions of the entire site volume. Thus, it contributes to the elimination of drilling cost for site investigation, to a more precise evaluation of the ground thermal performance and to the optimal installation design of GSHP systems.

Acknowledgments The thermal response test and the processing of the results were performed with the equipment of CRES and the personal contribution of Prof. B. Sanner. Our acknowledgments to Dr. G. Apostolopoulos for his valuable help to the geophysical work. Nomenclature Tf heat carrier mean fluid temperature [oC] Q injected heat power [W] k thermal conductivity [W/m,K] H effective borehole depth [m] t time from start [s] thermal diffusivity [mm.sec-1] rb borehole radius [m] Eulers constant [0,5772] Rb Borehole Thermal resistance [K/[W/m]] RE Electrical resistivity [.m] RT Thermal resistivity [m.K/W] Tsur Undisturbed initial temperature of the ground [oC] w moisture content [%] Sr Saturation [%] Pd bulk dry density [g/cm3] Gs specific gravity F sum of the gravel and sand fractions in the soil [%] Index a, s, w: air, solid, water faze References ASHRAE, 1999. Ap. Handbook, ch 31, 1-26 Bristow K.L., 1998.Agricultural and Forest Meteorology, vol. 89, 75-84. Cote J., Konrad J.M., 2005. Can. Ceotech., vol 42, 61-78. Johansen O., 1975. PhD Thesis, Institute for Kjoletechnik, 7034 Trondheim-NTH, Norway. Kavanaugh S.P., Rafferty K., 1997. ASHRAE, Atlanta. Kersten M.S.,1949. University of Minnesota, Institute of Technology, Bulletin No. 52, 1-225. Loke M.H., Bauker R.D., 1996. Geophys. Prosp., vol. 44, 131-152 Loke M.H., 1990. Software users manual, supplied by ABEM geophysical instrument of Sweden Oshner T. E., Horton R., and Ren T., 2001. Soil Science Society American Journal, vol. 65, 1641-1647 Peters-Lidard C. D.,1998. American Meteorological Society, vol. 55, 1209-1224 Sanner B., Erich M., Marc S.,Edgar G., 2007. European Geothermal Congress 2007 Unterhaching, Germany, 30 May-1 June 2007 Sanner B., Hellstrm G., Spitler J. Gehlin S., 2005. Proc. WGC 2005 Antalya, paper 1436,.1-9 Shan Xiong Chen, 2007. Heat and Mas Transfer, DOI 10.1007/s00231-007-0357-1 Sarah S., Bassetti S., Pahud D., Kohl T., 2007. Geothermics vol. 361, 41166 Singh A. K., Chaudhary D. R., 1995. International Journal of Heat and mass Transfer, vol 38, No. 12, 2297-2303 Singh N. H., Konchenapalli D., 2000. Experimental Thermal and Fluid Science,vol. 22 133-143 Singh D. N., Kuriyan J. S. Manthena K. C.,2001. Experimental Thermal and Fluid Science, vol. 25, 175-181. Sreedeep S., Reshma A.C., Singh D.N., 2005. Experimental Thermal and Fluid Science, vol. 29, 217226. Woodside W. Messer J. H., 1961. Journal of Applied Physics. vol 32, 1688-1699

k[2]

k[2]

k[1] k[1]