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Correlation study of shallow layer rock and soil thermal physical tests in laboratory and field
Geothermics 53 (2015) 508–516
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Correlation study of shallow layer rock and soil thermal physical tests in laboratory and field Ping Gao a , Yanjun Zhang a,b,∗ , Ziwang Yu a , Jingtao Fang a , Qing Zhang a a b
College of Construction Engineering, Jilin University, Changchun 130026, China Ministry of Education Key Laboratory of Groundwater Resources and Environment, Jilin University, Changchun 130000, China
a r t i c l e
i n f o
Article history: Received 31 December 2012 Accepted 17 September 2014 Keywords: Thermal physical parameters Thermal response test Laboratory test Analytic hierarchy process Correlation
a b s t r a c t A new method was proposed in this study to determine the correlation between laboratory and thermal response tests that are usually applied to examine the thermal physical parameters of shallow-layer rock and soil. Layer depth, water content, density, and permeability were found to be the primary factors that affect the discrepancy between the two tests. Analytic hierarchy process was then used to compute the weighted values of each factor, and the testing results of the thermal physical parameters in the laboratory were modified based on the weighted values. Field and modified laboratory thermal physical parameters and practical heat transferring process were simulated using the numerical model, and the discrepancies in the heat conduction capacity were similar under three conditions. Finally, the product of pipe depth and thermal conductivity was suggested to represent heat transfer capacity, and the computed uniform thermal conductivity of the laboratory after modification was proposed to be basically equal to the comprehensive thermal conductivity of the thermal response test. This study provides new insights in determining the thermal physical parameters of rock and soil layers. © 2014 Elsevier Ltd. All rights reserved.
1. Introduction The accurate measurement of the thermal physical parameters of rock and soil layers is a crucial step in the application of ground source heat pump (GSHP). The heat exchange capacity of the ground is determined by testing thermal physical parameters, such as thermal conductivity, specific heat capacity and thermal diffusivity. Thermal conductivity is a critical parameter that determines heat transfer capacity. Thermal physical parameters are determined by laboratory methods and thermal response tests (TRTs) (Wang et al., 2007; Chen, 2008; Abuel-Naga et al., 2009; Hao et al., 2011; Huang, 2012). The former consists of steady and transient states, which include need-probe (uncertainty, 2–3%), divided-bar (uncertainty, 4%), guarded hot plate (4%), and hot wire (uncertainty, 4–5%). The latter is an in situ technique that is widely adopted in GSHP application (Signorelli et al., 2007; Sharqawy, Said et al., 2009). However, laboratory tests are limited because they only provide every point value of samples within the borehole depth, in which several properties, such as structure and water content, have changed. Thus, the testing results do not fully reflect the on-site heat transfer capacity of rock and soil layers. The TRT measures the gross value of
∗ Corresponding author at: College of Construction Engineering, Jilin University, Changchun 130026, China. Tel.: +86 18943142020. E-mail address: [email protected] (Y. Zhang). http://dx.doi.org/10.1016/j.geothermics.2014.09.005 0375-6505/© 2014 Elsevier Ltd. All rights reserved.
thermal physical parameters within the ground, which could simulate the actual GSHP operation (Hu et al., 2009a,b; Beier, 2011). Hence, the TRT is the best choice to test the thermal physical parameters for designing a ground heat exchanger. However, the TRT is also affected by many factors such as test cycle, power supply stability, groundwater seepage, and so on (Bandos, 2009; Song, 2009; Witte, 2013). TRT has been paid increasing attention because of its importance in GSHP. Yavuzturk et al. (1999), Yavuzturk and Chiasson (2002), Zeng et al. (2002), Yu et al. (2006), and Guan et al. (2011) studied the theoretical models of TRTs. Field testing instruments are also improved and developed (Gehlin, 2002; Wang et al., 2007, 2009, 2010; Meng, 2012). Yu et al. (2003), Lim et al. (2007), Sharqawy, Mokheimer et al. (2009), Hu et al. (2009a,b), Guan et al. (2010), and Bandos et al. (2011) processed uncertain analysis for testing results. Wanger and Clauser (2005), and Wagner and Bayer (2012) analyzed and evaluated the TRT. However, only a few studies have focused on laboratory tests, and the differences between the two testing techniques are rarely reported (Yu and Fang, 2002; Fan et al., 2007; Wang et al., 2010; Huang, 2012; Barry-Macaulay et al., 2013). In addition, studies on the correlation of the two methods have not yet to be done. Combined with the thermal physical tests of some projects in Shanghai and Jiagedaqi, the discrepancy between the experimental results from laboratory tests and TRTs was analyzed. The primary factors that affect the thermal physical parameters were selected,
P. Gao et al. / Geothermics 53 (2015) 508–516
and the weighted vector of every influencing factor were determined using the analytic hierarchy process (AHP) (Saaty, 1980) as well as by comparing the two testing methods and analyzing the factors without considering in the laboratory tests. The thermal physical parameters of laboratory tests were modified based on the weighted values. The modified values could reflect the ground heat transfer capacity in the study area. Finally, the modified thermal physical parameters and the values of the TRTs were simulated with the simulation program developed by the authors to verify that the two conditions are basically similar in terms of heat transfer capacity and illustrate the applicability of the modified method. Two simulating results and the actual heat transfer process of the ground heat exchanger were also compared. The study indicates that use of laboratory thermal physical parameters can be more suitable, thereby providing a good supplement for in situ TRT and reference data for GSHP design.
2. Fundamental principle Physical properties are generally always affected in the process of obtaining rock and soil samples. This process causes the differences in the thermal conductivity in actual situations. Thus, the results from TRT are adopted in designing a GSHP system. Based on these conditions, a new method is proposed in which AHP is used to modify the laboratory test data, and inversion thermal conductivity is performed by considering the primary influencing factors. This method enables the modified data to reflect the ground heat conduction capacity as close to that of the TRT. Previous studies have shown that different factors had varying effects on the thermal physical parameters of rock and soil. The change in specific heat capacity slightly affects thermal conductivity (Hu, 2009; Li, 2009; Chang, 2011). When water content and density increase, their influence on thermal conductivity also increases. However, the influence of porosity presents contrasting results (Abu-Hamdeh, 2001, 2003; Li et al., 2009). The influence of ground water seepage on thermal conductivity is more obvious (Chiasson et al., 2000; Fujii et al., 2005; Fan et al., 2007; Bozdag and Paksoy, 2008; Hu, 2009; Lee and Lam, 2012). Thus, the following were considered in the present study: 1. Layer depth, water content, density, and permeability coefficient were selected as the main factors that affect the thermal physical parameter discrepancy between laboratory and field tests. 2. Detailed field exploration, in situ TRT, and laboratory tests were performed to obtain accurate geotechnical thermal physical parameters, physical parameters and lithology data. 3. The use of AHP could establish a hierarchical structure model of thermal conductivity, which could determine the weighted values of the influencing factors. 4. To verify the applicability of the modified method, three heat transfer conditions were simulated with the models of heat conduction and seepage. These conditions include the thermal physical parameters of laboratory tests before and after modification, the TRTs, and the practical ground heat exchange process of rock and soil layers. 2.1. AHP AHP can be divided into three stages in which the weights of the influencing factors in the thermal conductivity are analyzed (Deng et al., 2012; Kuzmana et al., 2013). Based on a scale from 1 to 9 (Table 1), which was suggested by Saaty (1980), the relative importance of pair-wise comparisons aij , i, j = 1, . . ., n, of elements i and j was evaluated and collected in the pair-wise comparison
509
Table 1 Fundamental scale of AHP (Saaty, 1980). Value aij
Description
1 3 5 7 9 2, 4, 6, 8
Elements i and j are equally important Elements i is slightly more important than element j Elements i is much more important than element j Elements i is proved to be more important than element j Elements i is absolutely more important than element j Middle values
Table 2 Average random consistency index (RI). n
RI
n
RI
1 2 3 4 5 6 7
0 0 0.52 0.89 1.12 1.24 1.36
8 9 10 11 12 13 14
1.41 1.46 1.49 1.52 1.54 1.56 1.58
matrix A. The inverse comparison was assigned a reciprocal value: aji = 1/aij .
⎡
a11
a12
···
a1n
⎤
⎢a ⎥ ⎢ 21 a22 · · · a2n ⎥ ⎥ ⎥ .. .. . . .. .. ⎦ ⎣ . .
A=⎢ ⎢
an1
an2
···
(1)
ann
where aij is the important degree of element i relative to element j. Then, the following values were calculated by Eqs. (2)–(5): vector of weights (ω), maximum eigenvalue (max ), and consistency ratio (CR), respectively. aij 1 , n n a k=1 kj n
ωi =
i = 1, 2, . . ., n
(2)
j=1
n
max =
i=1
((Aω)i /ωi )
(3)
n
CI =
max − n n−1
(4)
CR =
CI RI
(5)
where ωi is the weight value, n is the matrix order, CI is the consistency index, and RI is the average random consistency index (Table 2). Finally, Eqs. (6) and (7) were used to calculate the total hierarchy sorting and the corresponding consistency ratio, respectively. ωjL =
n1
ωiK ϕji ,
j = 1, 2, 3, . . ., n2
(6)
i=1
n1
L
CR =
i=1
(ωiK CIKL )
i=1
(ωiK RIKL )
n1
i
(7)
i
where ωiK is the total ordering weight vector of ith (1 ≤ i ≤ n1 ) factor Ki in the upper layer (K), and ϕji is the weighted value of jth (1 ≤ j ≤ n1 ) factor Lj in the lower layer (L) corresponding to Ki (when Lj and Ki are unrelated, ϕji = 0). ωiL is the total ordering weight vector of jth (1 ≤ j ≤ n1 ) factor Lj in the lower layer (L). CIKL and RIKL are the i
i
consistency and average random consistency indexes of the judgment matrix in the L layer corresponding to Ki , respectively. CRL is the total ordering random consistency ratio of the L layer.
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Table 3 Testing results of the laboratory tests. Sample name
Sampling depth (m)
Grayish yellow silty clay Mucky silty clay Gray mucky clay Gray clay Gray silty clay Straw yellow silty clay Gray clay Gray clay Gray clay Gray clay Gray silty clay Gray coarse sand Gray coarse sand Gray silty clay Gray silty sand
3.60–3.90 5.10–5.40 8.10–8.40 15.10–15.40 22.10–22.40 30.10–30.40 35.10–35.40 40.10–40.40 45.10–45.40 50.10–50.40 58.10–58.40 65.10–65.40 75.10–75.40 90.10–90.40 100.10–100.40
Physical properties
Thermal physical properties
Water content (%)
Density (g/cm3 )
Porosity
Thermal conductivity (W/(m ◦ C))
Mass specific heat capacity (kJ/(kg ◦ C))
Thermal diffusivity (10−6 m2 /s)
32.92 38.91 47.23 50.32 32.27 22.22 38.13 38.61 39.84 33.21 34.63 25.13 22.53 29.47 16.97
1.87 1.83 1.75 1.71 1.86 2.03 1.85 1.80 1.79 1.88 1.86 1.99 2.01 1.94 2.12
0.94 1.06 1.30 1.41 0.94 0.65 1.05 1.11 1.14 0.94 0.97 0.69 0.64 0.81 0.48
1.43 1.54 1.34 1.20 1.43 1.77 1.24 1.38 1.14 1.32 1.31 1.67 1.76 1.41 1.91
1.47 1.93 1.81 1.96 1.90 1.80 1.57 1.60 1.81 1.47 1.49 1.24 1.45 1.28 1.18
0.520 0.436 0.423 0.358 0.404 0.484 0.427 0.479 0.352 0.478 0.473 0.677 0.604 0.568 0.764
Table 4 Testing results of the field TRTs. Velocity in pipe (m/s)
Type
Initial temperature (◦ C)
Thermal conductivity (W/(m ◦ C))
Volumetric specific heat capacity (106 J/(m3 ◦ C))
Thermal diffusivity (10−6 m2 /s)
Hole thermal resistance ((m ◦ C)/W)
0.3
De32single-U De32double-U De25double-U
18.1 17.9 17.3
1.541 1.997 1.747
2.194 2.026 1.951
0.702 0.986 0.895
0.132 0.191 0.156
0.6
De32single-U De32double-U De25double-U
18.0 17.8 17.3
1.606 2.083 1.695
2.083 1.968 2.118
– – –
– – –
17.7
1.778
2.057
0.861
0.160
Average value
The heat conduction model was adopted for the calculated weighted values to simulate the TRTs and laboratory thermal physical parameters before and after modification.
∂(εf )
2.2. Mathematical model of heat transfer
∂t
Establishing the complete mathematical transfer model to simulate the practical heat transfer process of the ground heat exchanger is necessary. Convection and dispersion of heat transfer, which are similar to the mechanism of solute transport, follow Darcy’s law, the principle of mass conservation, and porous medium theory. However, formulating the complete coupled model is difficult because the process involves various factors of heat and mass transfer. Thus, assumptions were necessary for the establishment of the numerical model. The heat transport formula is written as follows: ∂(εf cf + (1 − ε)s cs )T ∂t
H∇T = ∇ (εf + (1 − ε)s )I ∇ T + ∇ εD − ∇ εf cf vT + q∗ cf T ∗ + qH
m3 /(m3 s); v is the pore velocity vector, m/s; and qH is the heat source rate intensity, W/m3 . The groundwater flow partial differential equation is written as
(8)
where ε is the effective porosity of the aquifer medium; cf is the fluid specific heat capacity, J/(kg ◦ C); cs is the porous medium specific heat capacity, J/(kg ◦ C); f is the fluid density, kg/m3 ; s is the porous medium density, kg/m3 ; f is the fluid thermal conductivity, W/(m ◦ C); s is the porous medium thermal conductivity, W/(m ◦ C); H is the thermal mechanical dispersion tensor, W/(m ◦ C); T is the D fluid and porous medium temperature, ◦ C; I is the identity matrix of rank 3; * is the density of the fluid source, kg/m3 ; T* is the temperature of the fluid source, ◦ C; q is the fluid source flow rate intensity, where the inflow is positive and the outflow is negative,
= ∇ f
k (∇ p + f g) + q∗
(9)
where p is the fluid pressure, Pa; k is the permeability tensor of the porous medium, m2 ; is the fluid viscosity, kg/(m s); g is the gravitational constant, m/s2 ; and t is the time, s.
3. Project example 1 3.1. Project overview The land area of the project in Shanghai is 50,578 m2 , and the total construction area is approximately 122,988 m2 . The ground and underground construction areas are approximately 61,593 and 61,395 m2 , respectively. To apply GSHP, thermal physical tests of rock and soil were performed in the region. The test involved six TRTs under different conditions in three boreholes and 15 laboratory thermal physical tests of rock and soil samples for the #1 borehole. Several physical properties of the samples were also measured. Tables 3 and 4 show the results of the in situ TRTs and laboratory tests. In the region, the foundation soil mainly consisted of clay, silt, and sand within the depth of 100 m below natural ground. Based on the borehole lithology data, the foundation soil could take in mucky clay (15 m), silty clay (15 m), clay (30 m), and sand (40 m). Moreover, the study region revealed unconfined and confined aquifers.
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511
Thermal conductivity A
Criteria Layer
Layer depth B1
Water content B2
Density B3
Permeability B4
Program Layer
Mucky clay C1
Clay C2
Silty clay C3
Sand C4
Fig. 1. Hierarchical structure model of the thermal conductivity.
Table 5 Weighted values of every influencing factor.
Table 6 Weighted values of every influencing factor judgment matrix.
Layer depth ω1
Water content ω2
Density ω3
Permeability ω4
0.4708
0.1715
0.0736
0.2841
Layer depth Water content Density Permeability
3.2. AHP weight determination 3.2.1. Establishing the hierarchical structure model of thermal conductivity Combined with geological conditions and thermal physical test results of the region in Shanghai, the main soil layer types for thermal conductivity are mucky clay, clay, silty clay, and sand. The main factors that influence the discrepancy in the thermal conductivity between laboratory and field tests are layer depth, water content, density, and permeability. The hierarchical structure model of the thermal conductivity is shown in Fig. 1. 3.2.2. Constructing judgment matrix, determining weights, and performing consistency tests Every factor of the criteria layer was compared, several experts were consulted, and past research results were referred to in this study. The thermal conductivity matrix A of the influencing factors of the target layer to the criteria layer was determined based on a scale from 1 to 9 (Table 1), as suggested by Saaty (1980) [Eq. (10)].
⎡
1
3
4
2
⎤
⎢ 1/3 1 3 1/2 ⎥ ⎥ ⎣ 1/4 1/3 1 1/4 ⎦
A=⎢
1/2
2
4
Judgment matrix
(10)
1
The weighted values of each factor were calculated based on Eq. (2), and Table 5 shows the results. The maximum eigenvalue can be calculated from the judgment matrix (10) based on Eq. (3), and the CR can be derived from Eq. (5). CR = 0.02 < 0.1. Therefore, the judgment matrix A satisfies the consistency requirement. Similarly, a judgment matrix of the criteria layer to the program layer was constructed, and the weights were calculated and checked for consistency. The weighted values of every judgment matrix were obtained (Table 6). The ratio of each soil type that affects the thermal conductivity were obtained by calculating the comprehensive weights based on Eq. (6). Table 7 shows the comprehensive weighted values. These judgment matrices satisfied the consistency requirements. Table 7 shows that the highest weighted value is sand, which is 0.4062. The lowest are mucky and silty clays, with basically similar values. The results indicate that pore connectivity and permeability
Weighted values ω1
ω2
ω3
ω4
0.1412 0.4658 0.1411 0.0941
0.2653 0.2771 0.1411 0.1578
0.1412 0.1611 0.2631 0.2471
0.4545 0.0960 0.4547 0.5010
Table 7 Comprehensive weighted values of every layer type. Mucky clay W1
Clay W2
Silty clay W3
Sand W4
0.1835
0.2266
0.1837
0.4062
of sand are better than those of the other three layer types, and the heat transfer is best in the sand layer. 3.3. Model verification The stratum of the study area was rather stable, and its initial average temperature was 17.7 ◦ C. In the TRTs, the diameter and depth of the three boreholes were 150 mm and 100 m, respectively. Single-U and double-U pipes were used, and the external and internal diameters were 32 and 25 mm, respectively (Table 4). The average values of the thermal conductivity and diffusivity of generalized four layers could be obtained (Table 8) based on the testing results of laboratory samples (Table 3). Table 8 also shows the thermal conductivity and diffusivity after modification based on the above-mentioned weighted values (Table 7). To verify the correctness of the weighted values, the numerical model of the ground heat exchanger was established based on the practical conditions of the project in Shanghai. The heat transfer capacity of the geotechnical layer with the thermal physical parameters of the laboratory tests before and after modification and the TRTs were simulated. The detailed model is as follows: 1. Numerical model: In the model diagram shown in Fig. 2, the width was 5 m, the depth was 100 m, and the model was composed of mucky clay (15 m), silty clay (15 m), clay (30 m), and sand (40 m) from the top down. 2. Initial condition: The initial temperature was 17.7 ◦ C, and the influence of season change was not considered. 3. Boundary condition: The temperature around the boundary was assumed to be fixed, and the top and bottom boundaries were insulated. 4. Meshing: In the model, the Z direction coordinate was downward, and uniform subdivision method was adopted. 5. Other settings: Heat source was set as the central node of the simulating region; the depth of the ground heat exchanger was
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Table 8 Thermal physical parameters of laboratory tests before and after modification. Layer type
Mucky clay Silty clay Clay Sand
Before modification
Weighted values
Thermal conductivity (W/(m ◦ C))
Thermal diffusivity (10−6 m2 /s)
1.44 1.27 1.60 1.72
4.30 × 10−7 4.34 × 10−7 4.44 × 10−7 6.41 × 10−7
After modification
0.1835 0.1837 0.2266 0.4062
Thermal conductivity (W/(m ◦ C))
Thermal diffusivity (10−6 m2 /s)
1.70 1.50 1.96 2.42
5.09 × 10−7 5.14 × 10−7 5.45 × 10−7 9.01 × 10−7
Table 9 Groundwater parameters. Viscosity (Pa s)
Expansion coefficient (1/◦ C)
Compression coefficient (MPa−1 )
Thermal conductivity (W/(m ◦ C))
Specific heat capacity (kJ/(kg ◦ C))
Seepage velocity (m/s)
Temperature (◦ C)
0.001
0.0002
0
0.6
4.182
1.73 × 10−7
18.02
Table 10 Thermal physical parameters of geotechnical layers. Layer type
Porosity
Density (kg/m3 )
Thermal conductivity (W/(m ◦ C))
Thermal diffusivity (10−6 m2 /s)
Volumetric specific heat capacity (106 J/(m3 ◦ C))
Mucky clay Silty clay Clay Sand
0.54 0.51 0.44 0.40
1790 1830 1945 2000
1.44 1.27 1.60 1.72
4.30 × 10−7 4.34 × 10−7 4.44 × 10−7 6.41 × 10−7
3.349 2.926 3.604 2.683
Fig. 2. Diagram of the numerical model.
Fig. 3. Contour of the field TRT numerical results.
95 m to simulate continuous operating conditions during the summer; the load was 3.5 kW, and the total time was 259,200 s, which is equivalent to 3 d. Based on the established model of the ground heat exchanger, simulations were performed for the thermal physical parameters of the TRTs and laboratory tests as well as the modified thermal physical parameters of the laboratory tests. When the TRTs were simulated, the model adopted the uniform layer and the thermal physical parameters of field test (Table 4), and Fig. 3 presents the contour of the simulated results. By contrast, in simulating the laboratory tests before and after modification, the thermal physical parameters adopted the average values of every layer (Table 8), and the contours of the simulated results are shown in Figs. 4 and 5.
Heat spread evenly along the center heat source in the ground when the in situ TRTs were simulated (Fig. 3). The section x = 2 m was selected, as shown in the red line, in which the distance was approximately 0.5 m from the central heat source. In the simulation depth range, the total heat flow when crossing the selected section was Q = 1606.9 J/(m s). The ground temperature field of Fig. 4 was divided into four sections because of the different thermal physical parameters of mucky clay, silty clay, clay, and sand, which is obviously different from Fig. 3. Heat transfer was observed more in the surrounding soil and rock layers with the increase in thermal conductivity. By contrast, heat accumulated around the central line. However, every part of the temperature field remained symmetrically
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Table 11 Thermal physical parameters of the Jiagedaqi region. Pipe type
Test hole number
Heating power (W)
Thermal conductivity (W/(m ◦ C))
Volumetric heat capacity (106 J/(m3 ◦ C))
Single-U
SK1
4000 6000
2.50 2.51
3.246. 3.187
Double-U
SK3
4000 6000
2.30 2.19
3.224 3.215
2.375
3.218
Average value
–
Table 12 Weighted values of comprehensive influencing factors.
Fig. 4. Contour of the laboratory numerical results before modification.
distributed at the center of the heat source. The total heat flow was Q = 1356.4 J/(m s) when crossing above the sectional plane, and the discrepancy between Figs. 3 and 4 was 15.6%. In summary, this discrepancy was only observed in the selected section. Thus, more discrepancies are expected in all study regions. These results
Fig. 5. Contour of the laboratory numerical results after modification.
Rounded gravel W1
Grit W2
Sandstone W3
Granite W4
0.2285
0.1799
0.2514
0.3402
illustrate that the thermal physical parameters of the laboratory tests only reflect a part of the heat transfer capacity, which indicates a huge gap compared with actual situations. Similar to Fig. 4, the temperature field in Fig. 5 was also divided into four parts. The thermal conductivity of every layer increased after considering main influencing factors. The heat was transferred to the ground more than the conditions in Fig. 4. The total heat flow was Q = 1587.7 J/(m s) when crossing above the sectional plane, and the discrepancy between Figs. 3 and 5 was 1.2%. When the whole study region was considered, the discrepancy between the two conditions was basically similar, and the error satisfied the requirements of engineering design. The calculated results show that the modified thermal physical parameters of the laboratory tests could reflect the heat transfer capacity of the rock and soil layers. To simulate the practical heat transfer process of GSHP, the numerical model of a ground heat exchanger should be established based on the actual project situations in Shanghai. The model was established similar to the aforementioned steps. However, the difference is that the groundwater flow was added from right to left in the sand layer to account for the influence of groundwater seepage. The detailed model diagram is shown in Fig. 6. The parameters necessary in the simulation can be obtained from the thermal physical tests, physical and mechanical property experiments, and in situ pumping and irrigation tests in the project (Tables 9 and 10).
Fig. 6. Diagram of the numerical model including groundwater.
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Table 13 Thermal physical parameters of laboratory before and after modification. Layer type
Before modification Thermal conductivity (W/(m ◦ C))
Weighted values
After modification Thermal conductivity (W/(m ◦ C))
Rounded gravel Grit Sandstone Granite
1.200 1.056 1.842 2.979
0.2285 0.1799 0.2514 0.3402
1.474 1.246 2.305 3.992
factor (1 − ), which is related to the degree of computational model generalization. K = H · ∗ = (h1 · 1 + h2 · 2 + · · · + hn · n )(1 − )
(11)
where H is the total depth of the rock and soil layers, m; * is the uniform thermal conductivity after modification, W/(m ◦ C); h1 , . . ., hn are the depths of each rock and soil layer after generalization, respectively, m; 1 , . . ., n are the thermal conductivities of the laboratory tests after modification corresponding to each rock and soil layer, respectively, W/(m ◦ C); and = (0.01–0.15) is the modified coefficient, which is related to the degree of generalization, and its value becomes higher when a simpler method of generalizing is used. Thus, K1 = H·* = (h1 ·1 + h2 ·2 + h3 ·3 + h4 ·4 )(1 − ) = 183.24 W/◦ C obtained for the modified thermal conductivity of laboratory tests (Table 8) corresponds to the uniform thermal conductivity * = 1.832 W/(m ◦ C), which is basically similar to = 1.778 W/(m ◦ C) of the TRTs. These findings indicate that the proposed method in this study is applicable, and the calculated uniform thermal conductivity is convenient for engineering design. 4. Project example 2 (Huang, 2012) Fig. 7. Contour of temperature field around ground heat exchanger.
The practical heat transfer process of GSHP was simulated using the established numerical model, and varying results of the temperature field were obtained. The changing contour of the geotechnical temperature field around the ground heat exchanger is shown in Fig. 7. The temperature fields of the top layers were symmetrically distributed along the central heat source without the influence of groundwater flow (Fig. 7). The heat exchange of the ground heat exchanger and the surrounding rock and soil layers were uniform. The temperature field of the sand layer was no longer symmetrically distributed along the central heat source, because of the influence of groundwater flow, and was slightly offset along the water-flow direction. Similar to Figs. 3 and 5, the total heat flow was Q = 1624.8 J/(m s) when the sectional plane of x = 2 m was crossed. The discrepancies between Figs. 3 and 5 were 1.1% and 2.3%, respectively. This phenomenon elucidates that the three situations have similar capacity in the heat transfer of ground rock and soil layers, which further verifies the feasibility of the proposed modified method. In addition, the key parameters are the depth of the ground heat exchanger and the thermal conductivity in the designing process of the GSHP system. Both products can represent the heat exchanging capacity of the rock and soil layers. For the TRTs, K0 = H· = 177.80 W/◦ C, where H is the total depth of the rock and soil layers, m; and is the thermal conductivity, W/(m ◦ C). Eq. (11) shows that the product was obtained when the thermal conductivity of each layer was multiplied by its depth for the modified thermal conductivity of the laboratory tests. The calculated value should be equal to the theoretical result of the TRTs. However, given the influence of various geological conditions and testing factors, the calculated results should be multiplied by a modified
4.1. Project overview The research area was located in the Jiagedaqi region of the Heilongjiang Province. Three shallow geothermal energy exploration holes in the region were arranged, and thermal physical tests were performed to investigate the thermo-physical properties of rock and soil. These tests included two in situ TRTs, with approximately 80 m borehole depth, and laboratory thermal physical tests of 20 samples. Table 11 shows the results of the TRTs. The drilling results show that the foundation soil of the research area consisted of miscellaneous fill, silty clay, rounded gravel, grit, sandstone, and granite below the ground within the 80 m depth. Based on the data of rock and soil layers, the foundation soil were divided into rounded gravel (11 m), grit (5 m), sandstone (25 m), and granite (39 m) from the top down. 4.2. Project application The weighted values and comprehensive weight of each influencing factor shown in Table 12 were based on the aforementioned AHP. The thermal conductivity obtained from the laboratory thermal physical tests was modified based on the calculated comprehensive weights (Table 13). The obtained value for the TRTs in the Jiagedaqi region when the depth of the ground heat exchanger was multiplied by the thermal conductivity was K0 = H· = 190.0 W/◦ C. The value for the modified thermal conductivity of laboratory tests was calculated using Eq. (11), as shown in Table 13. Thus, K1 = H·* = (h1 ·1 + h2 ·2 + h3 ·3 + h4 ·4 )(1 − ) = 205.11 W/◦ C, and the uniform thermal conductivity after modification was * = 2.564 W/(m ◦ C), which is basically similar to = 2.375 W/(m ◦ C) of the TRTs. Hence, the proposed method is feasible and can be used in practical project designs.
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5. Conclusions The following conclusions were drawn: 1. The primary factors that influence the discrepancy between TRTs and laboratory tests were analyzed by comparing the difference between the two tests combined with analysis of an actual situation in a project in Shanghai. These factors were layer depth, water content, density, and permeability. 2. AHP was used to determine the weights of every layer by combining the thermo-physical tests of the project in Shanghai. The comprehensive weights were 0.1835, 0.1837, 0.2266, and 0.4062 for the mucky clay, silty clay, clay, and sand layers, respectively. 3. The thermal physical parameters of the TRTs and modified thermal physical parameters of laboratory tests were simulated, and the discrepancy of the total heat flow was only 1.2% when similar selected sections were crossed. Furthermore, the practical heat transfer situation of a ground heat exchanger was simulated with a simulation program developed by the authors. The discrepancies of the total heat flow, which crossed the same sectional plane, were 1.1% and 2.3% between the simulated results and the two thermo-physical tests, respectively. This finding verifies that the three situations are similar in terms of capacity of heat transfer, and that the modified method is applicable. 4. In the GSHP design, the key parameters were the depth of ground heat exchanger and thermal conductivity. When the two parameters are multiplied, the results could represent the heat exchanging capacity of the rock and soil layer. The value of the thermo-physical parameters of the laboratory tests after modification was 183.24 W/◦ C in Shanghai. The calculated uniform thermal conductivity was 1.832 W/(m ◦ C), which is basically equal to 1.778 W/(m ◦ C) of the TRT. 5. The proposed method was applied to the thermal physical tests in the Jiagedaqi region in the Heilongjiang Province, and the study results further verified the applicability of the modified method. 6. In this study, the proposed method that modified the thermal physical parameters of the laboratory tests is a good supplement for in situ TRT and could replace TRT to a particular extent. The error of the modified method can satisfy the requirements of engineering design.
Acknowledgments This study was supported by the National High Technology Research and Development Program of China (863 Program) (No. 2012AA052801), the National Natural Science Foundation of China (No. 41372239), Specialized Research Fund for the Doctoral Program of Higher Education (No. 20110061110055), China Postdoctoral Science Foundation (No. 2014M551190), and the Shanghai Committee of Science and Technology, China (No. 10dz1202300).
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Geothermics journal homepage: www.elsevier.com/locate/geothermics
Correlation study of shallow layer rock and soil thermal physical tests in laboratory and field Ping Gao a , Yanjun Zhang a,b,∗ , Ziwang Yu a , Jingtao Fang a , Qing Zhang a a b
College of Construction Engineering, Jilin University, Changchun 130026, China Ministry of Education Key Laboratory of Groundwater Resources and Environment, Jilin University, Changchun 130000, China
a r t i c l e
i n f o
Article history: Received 31 December 2012 Accepted 17 September 2014 Keywords: Thermal physical parameters Thermal response test Laboratory test Analytic hierarchy process Correlation
a b s t r a c t A new method was proposed in this study to determine the correlation between laboratory and thermal response tests that are usually applied to examine the thermal physical parameters of shallow-layer rock and soil. Layer depth, water content, density, and permeability were found to be the primary factors that affect the discrepancy between the two tests. Analytic hierarchy process was then used to compute the weighted values of each factor, and the testing results of the thermal physical parameters in the laboratory were modified based on the weighted values. Field and modified laboratory thermal physical parameters and practical heat transferring process were simulated using the numerical model, and the discrepancies in the heat conduction capacity were similar under three conditions. Finally, the product of pipe depth and thermal conductivity was suggested to represent heat transfer capacity, and the computed uniform thermal conductivity of the laboratory after modification was proposed to be basically equal to the comprehensive thermal conductivity of the thermal response test. This study provides new insights in determining the thermal physical parameters of rock and soil layers. © 2014 Elsevier Ltd. All rights reserved.
1. Introduction The accurate measurement of the thermal physical parameters of rock and soil layers is a crucial step in the application of ground source heat pump (GSHP). The heat exchange capacity of the ground is determined by testing thermal physical parameters, such as thermal conductivity, specific heat capacity and thermal diffusivity. Thermal conductivity is a critical parameter that determines heat transfer capacity. Thermal physical parameters are determined by laboratory methods and thermal response tests (TRTs) (Wang et al., 2007; Chen, 2008; Abuel-Naga et al., 2009; Hao et al., 2011; Huang, 2012). The former consists of steady and transient states, which include need-probe (uncertainty, 2–3%), divided-bar (uncertainty, 4%), guarded hot plate (4%), and hot wire (uncertainty, 4–5%). The latter is an in situ technique that is widely adopted in GSHP application (Signorelli et al., 2007; Sharqawy, Said et al., 2009). However, laboratory tests are limited because they only provide every point value of samples within the borehole depth, in which several properties, such as structure and water content, have changed. Thus, the testing results do not fully reflect the on-site heat transfer capacity of rock and soil layers. The TRT measures the gross value of
∗ Corresponding author at: College of Construction Engineering, Jilin University, Changchun 130026, China. Tel.: +86 18943142020. E-mail address: [email protected] (Y. Zhang). http://dx.doi.org/10.1016/j.geothermics.2014.09.005 0375-6505/© 2014 Elsevier Ltd. All rights reserved.
thermal physical parameters within the ground, which could simulate the actual GSHP operation (Hu et al., 2009a,b; Beier, 2011). Hence, the TRT is the best choice to test the thermal physical parameters for designing a ground heat exchanger. However, the TRT is also affected by many factors such as test cycle, power supply stability, groundwater seepage, and so on (Bandos, 2009; Song, 2009; Witte, 2013). TRT has been paid increasing attention because of its importance in GSHP. Yavuzturk et al. (1999), Yavuzturk and Chiasson (2002), Zeng et al. (2002), Yu et al. (2006), and Guan et al. (2011) studied the theoretical models of TRTs. Field testing instruments are also improved and developed (Gehlin, 2002; Wang et al., 2007, 2009, 2010; Meng, 2012). Yu et al. (2003), Lim et al. (2007), Sharqawy, Mokheimer et al. (2009), Hu et al. (2009a,b), Guan et al. (2010), and Bandos et al. (2011) processed uncertain analysis for testing results. Wanger and Clauser (2005), and Wagner and Bayer (2012) analyzed and evaluated the TRT. However, only a few studies have focused on laboratory tests, and the differences between the two testing techniques are rarely reported (Yu and Fang, 2002; Fan et al., 2007; Wang et al., 2010; Huang, 2012; Barry-Macaulay et al., 2013). In addition, studies on the correlation of the two methods have not yet to be done. Combined with the thermal physical tests of some projects in Shanghai and Jiagedaqi, the discrepancy between the experimental results from laboratory tests and TRTs was analyzed. The primary factors that affect the thermal physical parameters were selected,
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and the weighted vector of every influencing factor were determined using the analytic hierarchy process (AHP) (Saaty, 1980) as well as by comparing the two testing methods and analyzing the factors without considering in the laboratory tests. The thermal physical parameters of laboratory tests were modified based on the weighted values. The modified values could reflect the ground heat transfer capacity in the study area. Finally, the modified thermal physical parameters and the values of the TRTs were simulated with the simulation program developed by the authors to verify that the two conditions are basically similar in terms of heat transfer capacity and illustrate the applicability of the modified method. Two simulating results and the actual heat transfer process of the ground heat exchanger were also compared. The study indicates that use of laboratory thermal physical parameters can be more suitable, thereby providing a good supplement for in situ TRT and reference data for GSHP design.
2. Fundamental principle Physical properties are generally always affected in the process of obtaining rock and soil samples. This process causes the differences in the thermal conductivity in actual situations. Thus, the results from TRT are adopted in designing a GSHP system. Based on these conditions, a new method is proposed in which AHP is used to modify the laboratory test data, and inversion thermal conductivity is performed by considering the primary influencing factors. This method enables the modified data to reflect the ground heat conduction capacity as close to that of the TRT. Previous studies have shown that different factors had varying effects on the thermal physical parameters of rock and soil. The change in specific heat capacity slightly affects thermal conductivity (Hu, 2009; Li, 2009; Chang, 2011). When water content and density increase, their influence on thermal conductivity also increases. However, the influence of porosity presents contrasting results (Abu-Hamdeh, 2001, 2003; Li et al., 2009). The influence of ground water seepage on thermal conductivity is more obvious (Chiasson et al., 2000; Fujii et al., 2005; Fan et al., 2007; Bozdag and Paksoy, 2008; Hu, 2009; Lee and Lam, 2012). Thus, the following were considered in the present study: 1. Layer depth, water content, density, and permeability coefficient were selected as the main factors that affect the thermal physical parameter discrepancy between laboratory and field tests. 2. Detailed field exploration, in situ TRT, and laboratory tests were performed to obtain accurate geotechnical thermal physical parameters, physical parameters and lithology data. 3. The use of AHP could establish a hierarchical structure model of thermal conductivity, which could determine the weighted values of the influencing factors. 4. To verify the applicability of the modified method, three heat transfer conditions were simulated with the models of heat conduction and seepage. These conditions include the thermal physical parameters of laboratory tests before and after modification, the TRTs, and the practical ground heat exchange process of rock and soil layers. 2.1. AHP AHP can be divided into three stages in which the weights of the influencing factors in the thermal conductivity are analyzed (Deng et al., 2012; Kuzmana et al., 2013). Based on a scale from 1 to 9 (Table 1), which was suggested by Saaty (1980), the relative importance of pair-wise comparisons aij , i, j = 1, . . ., n, of elements i and j was evaluated and collected in the pair-wise comparison
509
Table 1 Fundamental scale of AHP (Saaty, 1980). Value aij
Description
1 3 5 7 9 2, 4, 6, 8
Elements i and j are equally important Elements i is slightly more important than element j Elements i is much more important than element j Elements i is proved to be more important than element j Elements i is absolutely more important than element j Middle values
Table 2 Average random consistency index (RI). n
RI
n
RI
1 2 3 4 5 6 7
0 0 0.52 0.89 1.12 1.24 1.36
8 9 10 11 12 13 14
1.41 1.46 1.49 1.52 1.54 1.56 1.58
matrix A. The inverse comparison was assigned a reciprocal value: aji = 1/aij .
⎡
a11
a12
···
a1n
⎤
⎢a ⎥ ⎢ 21 a22 · · · a2n ⎥ ⎥ ⎥ .. .. . . .. .. ⎦ ⎣ . .
A=⎢ ⎢
an1
an2
···
(1)
ann
where aij is the important degree of element i relative to element j. Then, the following values were calculated by Eqs. (2)–(5): vector of weights (ω), maximum eigenvalue (max ), and consistency ratio (CR), respectively. aij 1 , n n a k=1 kj n
ωi =
i = 1, 2, . . ., n
(2)
j=1
n
max =
i=1
((Aω)i /ωi )
(3)
n
CI =
max − n n−1
(4)
CR =
CI RI
(5)
where ωi is the weight value, n is the matrix order, CI is the consistency index, and RI is the average random consistency index (Table 2). Finally, Eqs. (6) and (7) were used to calculate the total hierarchy sorting and the corresponding consistency ratio, respectively. ωjL =
n1
ωiK ϕji ,
j = 1, 2, 3, . . ., n2
(6)
i=1
n1
L
CR =
i=1
(ωiK CIKL )
i=1
(ωiK RIKL )
n1
i
(7)
i
where ωiK is the total ordering weight vector of ith (1 ≤ i ≤ n1 ) factor Ki in the upper layer (K), and ϕji is the weighted value of jth (1 ≤ j ≤ n1 ) factor Lj in the lower layer (L) corresponding to Ki (when Lj and Ki are unrelated, ϕji = 0). ωiL is the total ordering weight vector of jth (1 ≤ j ≤ n1 ) factor Lj in the lower layer (L). CIKL and RIKL are the i
i
consistency and average random consistency indexes of the judgment matrix in the L layer corresponding to Ki , respectively. CRL is the total ordering random consistency ratio of the L layer.
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Table 3 Testing results of the laboratory tests. Sample name
Sampling depth (m)
Grayish yellow silty clay Mucky silty clay Gray mucky clay Gray clay Gray silty clay Straw yellow silty clay Gray clay Gray clay Gray clay Gray clay Gray silty clay Gray coarse sand Gray coarse sand Gray silty clay Gray silty sand
3.60–3.90 5.10–5.40 8.10–8.40 15.10–15.40 22.10–22.40 30.10–30.40 35.10–35.40 40.10–40.40 45.10–45.40 50.10–50.40 58.10–58.40 65.10–65.40 75.10–75.40 90.10–90.40 100.10–100.40
Physical properties
Thermal physical properties
Water content (%)
Density (g/cm3 )
Porosity
Thermal conductivity (W/(m ◦ C))
Mass specific heat capacity (kJ/(kg ◦ C))
Thermal diffusivity (10−6 m2 /s)
32.92 38.91 47.23 50.32 32.27 22.22 38.13 38.61 39.84 33.21 34.63 25.13 22.53 29.47 16.97
1.87 1.83 1.75 1.71 1.86 2.03 1.85 1.80 1.79 1.88 1.86 1.99 2.01 1.94 2.12
0.94 1.06 1.30 1.41 0.94 0.65 1.05 1.11 1.14 0.94 0.97 0.69 0.64 0.81 0.48
1.43 1.54 1.34 1.20 1.43 1.77 1.24 1.38 1.14 1.32 1.31 1.67 1.76 1.41 1.91
1.47 1.93 1.81 1.96 1.90 1.80 1.57 1.60 1.81 1.47 1.49 1.24 1.45 1.28 1.18
0.520 0.436 0.423 0.358 0.404 0.484 0.427 0.479 0.352 0.478 0.473 0.677 0.604 0.568 0.764
Table 4 Testing results of the field TRTs. Velocity in pipe (m/s)
Type
Initial temperature (◦ C)
Thermal conductivity (W/(m ◦ C))
Volumetric specific heat capacity (106 J/(m3 ◦ C))
Thermal diffusivity (10−6 m2 /s)
Hole thermal resistance ((m ◦ C)/W)
0.3
De32single-U De32double-U De25double-U
18.1 17.9 17.3
1.541 1.997 1.747
2.194 2.026 1.951
0.702 0.986 0.895
0.132 0.191 0.156
0.6
De32single-U De32double-U De25double-U
18.0 17.8 17.3
1.606 2.083 1.695
2.083 1.968 2.118
– – –
– – –
17.7
1.778
2.057
0.861
0.160
Average value
The heat conduction model was adopted for the calculated weighted values to simulate the TRTs and laboratory thermal physical parameters before and after modification.
∂(εf )
2.2. Mathematical model of heat transfer
∂t
Establishing the complete mathematical transfer model to simulate the practical heat transfer process of the ground heat exchanger is necessary. Convection and dispersion of heat transfer, which are similar to the mechanism of solute transport, follow Darcy’s law, the principle of mass conservation, and porous medium theory. However, formulating the complete coupled model is difficult because the process involves various factors of heat and mass transfer. Thus, assumptions were necessary for the establishment of the numerical model. The heat transport formula is written as follows: ∂(εf cf + (1 − ε)s cs )T ∂t
H∇T = ∇ (εf + (1 − ε)s )I ∇ T + ∇ εD − ∇ εf cf vT + q∗ cf T ∗ + qH
m3 /(m3 s); v is the pore velocity vector, m/s; and qH is the heat source rate intensity, W/m3 . The groundwater flow partial differential equation is written as
(8)
where ε is the effective porosity of the aquifer medium; cf is the fluid specific heat capacity, J/(kg ◦ C); cs is the porous medium specific heat capacity, J/(kg ◦ C); f is the fluid density, kg/m3 ; s is the porous medium density, kg/m3 ; f is the fluid thermal conductivity, W/(m ◦ C); s is the porous medium thermal conductivity, W/(m ◦ C); H is the thermal mechanical dispersion tensor, W/(m ◦ C); T is the D fluid and porous medium temperature, ◦ C; I is the identity matrix of rank 3; * is the density of the fluid source, kg/m3 ; T* is the temperature of the fluid source, ◦ C; q is the fluid source flow rate intensity, where the inflow is positive and the outflow is negative,
= ∇ f
k (∇ p + f g) + q∗
(9)
where p is the fluid pressure, Pa; k is the permeability tensor of the porous medium, m2 ; is the fluid viscosity, kg/(m s); g is the gravitational constant, m/s2 ; and t is the time, s.
3. Project example 1 3.1. Project overview The land area of the project in Shanghai is 50,578 m2 , and the total construction area is approximately 122,988 m2 . The ground and underground construction areas are approximately 61,593 and 61,395 m2 , respectively. To apply GSHP, thermal physical tests of rock and soil were performed in the region. The test involved six TRTs under different conditions in three boreholes and 15 laboratory thermal physical tests of rock and soil samples for the #1 borehole. Several physical properties of the samples were also measured. Tables 3 and 4 show the results of the in situ TRTs and laboratory tests. In the region, the foundation soil mainly consisted of clay, silt, and sand within the depth of 100 m below natural ground. Based on the borehole lithology data, the foundation soil could take in mucky clay (15 m), silty clay (15 m), clay (30 m), and sand (40 m). Moreover, the study region revealed unconfined and confined aquifers.
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511
Thermal conductivity A
Criteria Layer
Layer depth B1
Water content B2
Density B3
Permeability B4
Program Layer
Mucky clay C1
Clay C2
Silty clay C3
Sand C4
Fig. 1. Hierarchical structure model of the thermal conductivity.
Table 5 Weighted values of every influencing factor.
Table 6 Weighted values of every influencing factor judgment matrix.
Layer depth ω1
Water content ω2
Density ω3
Permeability ω4
0.4708
0.1715
0.0736
0.2841
Layer depth Water content Density Permeability
3.2. AHP weight determination 3.2.1. Establishing the hierarchical structure model of thermal conductivity Combined with geological conditions and thermal physical test results of the region in Shanghai, the main soil layer types for thermal conductivity are mucky clay, clay, silty clay, and sand. The main factors that influence the discrepancy in the thermal conductivity between laboratory and field tests are layer depth, water content, density, and permeability. The hierarchical structure model of the thermal conductivity is shown in Fig. 1. 3.2.2. Constructing judgment matrix, determining weights, and performing consistency tests Every factor of the criteria layer was compared, several experts were consulted, and past research results were referred to in this study. The thermal conductivity matrix A of the influencing factors of the target layer to the criteria layer was determined based on a scale from 1 to 9 (Table 1), as suggested by Saaty (1980) [Eq. (10)].
⎡
1
3
4
2
⎤
⎢ 1/3 1 3 1/2 ⎥ ⎥ ⎣ 1/4 1/3 1 1/4 ⎦
A=⎢
1/2
2
4
Judgment matrix
(10)
1
The weighted values of each factor were calculated based on Eq. (2), and Table 5 shows the results. The maximum eigenvalue can be calculated from the judgment matrix (10) based on Eq. (3), and the CR can be derived from Eq. (5). CR = 0.02 < 0.1. Therefore, the judgment matrix A satisfies the consistency requirement. Similarly, a judgment matrix of the criteria layer to the program layer was constructed, and the weights were calculated and checked for consistency. The weighted values of every judgment matrix were obtained (Table 6). The ratio of each soil type that affects the thermal conductivity were obtained by calculating the comprehensive weights based on Eq. (6). Table 7 shows the comprehensive weighted values. These judgment matrices satisfied the consistency requirements. Table 7 shows that the highest weighted value is sand, which is 0.4062. The lowest are mucky and silty clays, with basically similar values. The results indicate that pore connectivity and permeability
Weighted values ω1
ω2
ω3
ω4
0.1412 0.4658 0.1411 0.0941
0.2653 0.2771 0.1411 0.1578
0.1412 0.1611 0.2631 0.2471
0.4545 0.0960 0.4547 0.5010
Table 7 Comprehensive weighted values of every layer type. Mucky clay W1
Clay W2
Silty clay W3
Sand W4
0.1835
0.2266
0.1837
0.4062
of sand are better than those of the other three layer types, and the heat transfer is best in the sand layer. 3.3. Model verification The stratum of the study area was rather stable, and its initial average temperature was 17.7 ◦ C. In the TRTs, the diameter and depth of the three boreholes were 150 mm and 100 m, respectively. Single-U and double-U pipes were used, and the external and internal diameters were 32 and 25 mm, respectively (Table 4). The average values of the thermal conductivity and diffusivity of generalized four layers could be obtained (Table 8) based on the testing results of laboratory samples (Table 3). Table 8 also shows the thermal conductivity and diffusivity after modification based on the above-mentioned weighted values (Table 7). To verify the correctness of the weighted values, the numerical model of the ground heat exchanger was established based on the practical conditions of the project in Shanghai. The heat transfer capacity of the geotechnical layer with the thermal physical parameters of the laboratory tests before and after modification and the TRTs were simulated. The detailed model is as follows: 1. Numerical model: In the model diagram shown in Fig. 2, the width was 5 m, the depth was 100 m, and the model was composed of mucky clay (15 m), silty clay (15 m), clay (30 m), and sand (40 m) from the top down. 2. Initial condition: The initial temperature was 17.7 ◦ C, and the influence of season change was not considered. 3. Boundary condition: The temperature around the boundary was assumed to be fixed, and the top and bottom boundaries were insulated. 4. Meshing: In the model, the Z direction coordinate was downward, and uniform subdivision method was adopted. 5. Other settings: Heat source was set as the central node of the simulating region; the depth of the ground heat exchanger was
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Table 8 Thermal physical parameters of laboratory tests before and after modification. Layer type
Mucky clay Silty clay Clay Sand
Before modification
Weighted values
Thermal conductivity (W/(m ◦ C))
Thermal diffusivity (10−6 m2 /s)
1.44 1.27 1.60 1.72
4.30 × 10−7 4.34 × 10−7 4.44 × 10−7 6.41 × 10−7
After modification
0.1835 0.1837 0.2266 0.4062
Thermal conductivity (W/(m ◦ C))
Thermal diffusivity (10−6 m2 /s)
1.70 1.50 1.96 2.42
5.09 × 10−7 5.14 × 10−7 5.45 × 10−7 9.01 × 10−7
Table 9 Groundwater parameters. Viscosity (Pa s)
Expansion coefficient (1/◦ C)
Compression coefficient (MPa−1 )
Thermal conductivity (W/(m ◦ C))
Specific heat capacity (kJ/(kg ◦ C))
Seepage velocity (m/s)
Temperature (◦ C)
0.001
0.0002
0
0.6
4.182
1.73 × 10−7
18.02
Table 10 Thermal physical parameters of geotechnical layers. Layer type
Porosity
Density (kg/m3 )
Thermal conductivity (W/(m ◦ C))
Thermal diffusivity (10−6 m2 /s)
Volumetric specific heat capacity (106 J/(m3 ◦ C))
Mucky clay Silty clay Clay Sand
0.54 0.51 0.44 0.40
1790 1830 1945 2000
1.44 1.27 1.60 1.72
4.30 × 10−7 4.34 × 10−7 4.44 × 10−7 6.41 × 10−7
3.349 2.926 3.604 2.683
Fig. 2. Diagram of the numerical model.
Fig. 3. Contour of the field TRT numerical results.
95 m to simulate continuous operating conditions during the summer; the load was 3.5 kW, and the total time was 259,200 s, which is equivalent to 3 d. Based on the established model of the ground heat exchanger, simulations were performed for the thermal physical parameters of the TRTs and laboratory tests as well as the modified thermal physical parameters of the laboratory tests. When the TRTs were simulated, the model adopted the uniform layer and the thermal physical parameters of field test (Table 4), and Fig. 3 presents the contour of the simulated results. By contrast, in simulating the laboratory tests before and after modification, the thermal physical parameters adopted the average values of every layer (Table 8), and the contours of the simulated results are shown in Figs. 4 and 5.
Heat spread evenly along the center heat source in the ground when the in situ TRTs were simulated (Fig. 3). The section x = 2 m was selected, as shown in the red line, in which the distance was approximately 0.5 m from the central heat source. In the simulation depth range, the total heat flow when crossing the selected section was Q = 1606.9 J/(m s). The ground temperature field of Fig. 4 was divided into four sections because of the different thermal physical parameters of mucky clay, silty clay, clay, and sand, which is obviously different from Fig. 3. Heat transfer was observed more in the surrounding soil and rock layers with the increase in thermal conductivity. By contrast, heat accumulated around the central line. However, every part of the temperature field remained symmetrically
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Table 11 Thermal physical parameters of the Jiagedaqi region. Pipe type
Test hole number
Heating power (W)
Thermal conductivity (W/(m ◦ C))
Volumetric heat capacity (106 J/(m3 ◦ C))
Single-U
SK1
4000 6000
2.50 2.51
3.246. 3.187
Double-U
SK3
4000 6000
2.30 2.19
3.224 3.215
2.375
3.218
Average value
–
Table 12 Weighted values of comprehensive influencing factors.
Fig. 4. Contour of the laboratory numerical results before modification.
distributed at the center of the heat source. The total heat flow was Q = 1356.4 J/(m s) when crossing above the sectional plane, and the discrepancy between Figs. 3 and 4 was 15.6%. In summary, this discrepancy was only observed in the selected section. Thus, more discrepancies are expected in all study regions. These results
Fig. 5. Contour of the laboratory numerical results after modification.
Rounded gravel W1
Grit W2
Sandstone W3
Granite W4
0.2285
0.1799
0.2514
0.3402
illustrate that the thermal physical parameters of the laboratory tests only reflect a part of the heat transfer capacity, which indicates a huge gap compared with actual situations. Similar to Fig. 4, the temperature field in Fig. 5 was also divided into four parts. The thermal conductivity of every layer increased after considering main influencing factors. The heat was transferred to the ground more than the conditions in Fig. 4. The total heat flow was Q = 1587.7 J/(m s) when crossing above the sectional plane, and the discrepancy between Figs. 3 and 5 was 1.2%. When the whole study region was considered, the discrepancy between the two conditions was basically similar, and the error satisfied the requirements of engineering design. The calculated results show that the modified thermal physical parameters of the laboratory tests could reflect the heat transfer capacity of the rock and soil layers. To simulate the practical heat transfer process of GSHP, the numerical model of a ground heat exchanger should be established based on the actual project situations in Shanghai. The model was established similar to the aforementioned steps. However, the difference is that the groundwater flow was added from right to left in the sand layer to account for the influence of groundwater seepage. The detailed model diagram is shown in Fig. 6. The parameters necessary in the simulation can be obtained from the thermal physical tests, physical and mechanical property experiments, and in situ pumping and irrigation tests in the project (Tables 9 and 10).
Fig. 6. Diagram of the numerical model including groundwater.
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Table 13 Thermal physical parameters of laboratory before and after modification. Layer type
Before modification Thermal conductivity (W/(m ◦ C))
Weighted values
After modification Thermal conductivity (W/(m ◦ C))
Rounded gravel Grit Sandstone Granite
1.200 1.056 1.842 2.979
0.2285 0.1799 0.2514 0.3402
1.474 1.246 2.305 3.992
factor (1 − ), which is related to the degree of computational model generalization. K = H · ∗ = (h1 · 1 + h2 · 2 + · · · + hn · n )(1 − )
(11)
where H is the total depth of the rock and soil layers, m; * is the uniform thermal conductivity after modification, W/(m ◦ C); h1 , . . ., hn are the depths of each rock and soil layer after generalization, respectively, m; 1 , . . ., n are the thermal conductivities of the laboratory tests after modification corresponding to each rock and soil layer, respectively, W/(m ◦ C); and = (0.01–0.15) is the modified coefficient, which is related to the degree of generalization, and its value becomes higher when a simpler method of generalizing is used. Thus, K1 = H·* = (h1 ·1 + h2 ·2 + h3 ·3 + h4 ·4 )(1 − ) = 183.24 W/◦ C obtained for the modified thermal conductivity of laboratory tests (Table 8) corresponds to the uniform thermal conductivity * = 1.832 W/(m ◦ C), which is basically similar to = 1.778 W/(m ◦ C) of the TRTs. These findings indicate that the proposed method in this study is applicable, and the calculated uniform thermal conductivity is convenient for engineering design. 4. Project example 2 (Huang, 2012) Fig. 7. Contour of temperature field around ground heat exchanger.
The practical heat transfer process of GSHP was simulated using the established numerical model, and varying results of the temperature field were obtained. The changing contour of the geotechnical temperature field around the ground heat exchanger is shown in Fig. 7. The temperature fields of the top layers were symmetrically distributed along the central heat source without the influence of groundwater flow (Fig. 7). The heat exchange of the ground heat exchanger and the surrounding rock and soil layers were uniform. The temperature field of the sand layer was no longer symmetrically distributed along the central heat source, because of the influence of groundwater flow, and was slightly offset along the water-flow direction. Similar to Figs. 3 and 5, the total heat flow was Q = 1624.8 J/(m s) when the sectional plane of x = 2 m was crossed. The discrepancies between Figs. 3 and 5 were 1.1% and 2.3%, respectively. This phenomenon elucidates that the three situations have similar capacity in the heat transfer of ground rock and soil layers, which further verifies the feasibility of the proposed modified method. In addition, the key parameters are the depth of the ground heat exchanger and the thermal conductivity in the designing process of the GSHP system. Both products can represent the heat exchanging capacity of the rock and soil layers. For the TRTs, K0 = H· = 177.80 W/◦ C, where H is the total depth of the rock and soil layers, m; and is the thermal conductivity, W/(m ◦ C). Eq. (11) shows that the product was obtained when the thermal conductivity of each layer was multiplied by its depth for the modified thermal conductivity of the laboratory tests. The calculated value should be equal to the theoretical result of the TRTs. However, given the influence of various geological conditions and testing factors, the calculated results should be multiplied by a modified
4.1. Project overview The research area was located in the Jiagedaqi region of the Heilongjiang Province. Three shallow geothermal energy exploration holes in the region were arranged, and thermal physical tests were performed to investigate the thermo-physical properties of rock and soil. These tests included two in situ TRTs, with approximately 80 m borehole depth, and laboratory thermal physical tests of 20 samples. Table 11 shows the results of the TRTs. The drilling results show that the foundation soil of the research area consisted of miscellaneous fill, silty clay, rounded gravel, grit, sandstone, and granite below the ground within the 80 m depth. Based on the data of rock and soil layers, the foundation soil were divided into rounded gravel (11 m), grit (5 m), sandstone (25 m), and granite (39 m) from the top down. 4.2. Project application The weighted values and comprehensive weight of each influencing factor shown in Table 12 were based on the aforementioned AHP. The thermal conductivity obtained from the laboratory thermal physical tests was modified based on the calculated comprehensive weights (Table 13). The obtained value for the TRTs in the Jiagedaqi region when the depth of the ground heat exchanger was multiplied by the thermal conductivity was K0 = H· = 190.0 W/◦ C. The value for the modified thermal conductivity of laboratory tests was calculated using Eq. (11), as shown in Table 13. Thus, K1 = H·* = (h1 ·1 + h2 ·2 + h3 ·3 + h4 ·4 )(1 − ) = 205.11 W/◦ C, and the uniform thermal conductivity after modification was * = 2.564 W/(m ◦ C), which is basically similar to = 2.375 W/(m ◦ C) of the TRTs. Hence, the proposed method is feasible and can be used in practical project designs.
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5. Conclusions The following conclusions were drawn: 1. The primary factors that influence the discrepancy between TRTs and laboratory tests were analyzed by comparing the difference between the two tests combined with analysis of an actual situation in a project in Shanghai. These factors were layer depth, water content, density, and permeability. 2. AHP was used to determine the weights of every layer by combining the thermo-physical tests of the project in Shanghai. The comprehensive weights were 0.1835, 0.1837, 0.2266, and 0.4062 for the mucky clay, silty clay, clay, and sand layers, respectively. 3. The thermal physical parameters of the TRTs and modified thermal physical parameters of laboratory tests were simulated, and the discrepancy of the total heat flow was only 1.2% when similar selected sections were crossed. Furthermore, the practical heat transfer situation of a ground heat exchanger was simulated with a simulation program developed by the authors. The discrepancies of the total heat flow, which crossed the same sectional plane, were 1.1% and 2.3% between the simulated results and the two thermo-physical tests, respectively. This finding verifies that the three situations are similar in terms of capacity of heat transfer, and that the modified method is applicable. 4. In the GSHP design, the key parameters were the depth of ground heat exchanger and thermal conductivity. When the two parameters are multiplied, the results could represent the heat exchanging capacity of the rock and soil layer. The value of the thermo-physical parameters of the laboratory tests after modification was 183.24 W/◦ C in Shanghai. The calculated uniform thermal conductivity was 1.832 W/(m ◦ C), which is basically equal to 1.778 W/(m ◦ C) of the TRT. 5. The proposed method was applied to the thermal physical tests in the Jiagedaqi region in the Heilongjiang Province, and the study results further verified the applicability of the modified method. 6. In this study, the proposed method that modified the thermal physical parameters of the laboratory tests is a good supplement for in situ TRT and could replace TRT to a particular extent. The error of the modified method can satisfy the requirements of engineering design.
Acknowledgments This study was supported by the National High Technology Research and Development Program of China (863 Program) (No. 2012AA052801), the National Natural Science Foundation of China (No. 41372239), Specialized Research Fund for the Doctoral Program of Higher Education (No. 20110061110055), China Postdoctoral Science Foundation (No. 2014M551190), and the Shanghai Committee of Science and Technology, China (No. 10dz1202300).
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