EVALUATION METHOD OF GROUND WATER VELOCITY APPLYING THE GRADIENT OF THERMAL RESPONSE

Transcription

1 EVALUATION METHOD OF GROUND WATER VELOCITY APPLYING THE GRADIENT OF THERMAL RESPONSE T. Katsura Faculty of Environmental Engineering, The University of Kitakyushu Kitakyushu , Japan Tel: Y. Nakamura Nippon Steel Engineering Tokyo Japan S. Hori, T. Okawada, K. Nagano Hokkaido University Sapporo , Japan ABSTRACT The authors have introduced a practical method for measuring the velocity of groundwater based on the gradient of thermal response. Three types of field experiments were conducted, namely, the thermal probe method, heating well method, and thermal response test. With respect to the thermal probe method, first, an experiment was conducted to calibrate the probe; then, a field experiment was conducted to determine groundwater velocity. The groundwater velocities in the field, obtained by the thermal probe method, were 0~200 m/year and they were in good agreement with the velocities obtained using the conventional method. Thus, it was ascertained that the thermal probe method is effective for evaluating groundwater velocity. 1. INTRODUCTION In order that the effect of groundwater be reflected in the design of ground-source heat pump (GSHP) systems and underground thermal storage systems, it is essential to determine groundwater velocity at the point where the systems are installed. An example of a conventional groundwater velocity measurement method would be the one in which the electrical conductivity is damped. In this method, a salt solution is infused into the observation well and the electrical conductivity in the well is measured. However, in this case, it is difficult to rapidly measure the groundwater velocities at points with varying depths because boring and cleaning of the observation well are essential. Therefore, an alternative method that can rapidly measure groundwater velocities at several points is required. The authors previously demonstrated that under constant heat generation in the probe, the temperature variations in groundwater caused by the flow of groundwater depend on its velocity (Katsura et al, 2006). In addition, a method for measuring the velocity of groundwater by using the variation in temperature gradient of groundwater was suggested (Katsura et al, 2006).

2 This paper describes the field tests conducted to determine the most suitable method for measuring the velocity of groundwater. First, the outlines of the methods of measurement and field tests are introduced. Next, with respect to the test method that uses a thermal probe, the relation between groundwater velocity and the variation in temperature gradient is clarified using the results of the laboratory experiment. Moreover, by using the results of the laboratory experiment, groundwater velocities in the field are calculated. Then, the groundwater velocities are compared to the ones estimated by the conventional method and the possibility of the actual use of the new method is discussed. 2. OUTLINE OF MEASUREMENT Outline of measurement When constant heat is generated from a heat source (line or cylindrical), the effect of groundwater flow on the temperature response depends on the velocity of groundwater. The authors carried out a laboratory experiment using a thermal probe that can generate constant heat and related experimental apparatus that can simulate groundwater flow in a sand layer (Katsura et al, 2006). Figure 1 shows the temperature variations in the thermal probe buried in the sand layer for varying groundwater velocities. The temperature increases linearly according to the logarithm of the elapsed time if the groundwater is still. With an increase in the velocity of groundwater, the temperature variations become smaller. By using Equation (1), the variation in the temperature gradient of thermal probe with respect to the elapsed time, which is shown in Figure 2, can be obtained. k () t () t T ( t / m) T = (1) ln( m) The value m is an arbitrary constant. When we use a logarithmic y-axis as shown in Figure 2, the variations in the temperature gradient are linear. From this result linearity of the variations in the gradient, the temperature gradient with respect to the elapsed time is approximated as follows: k nt () t ce = (c, n: constant) (2) Figure 3 shows the relation between the measured groundwater velocity and the coefficient of gradient n obtained from Figure 2. It is apparent from Figure 3 that the groundwater velocity shows a strong correlation with the coefficient n. Consequently, the following relational expression can be derived. b u = an (a, b: constant) (3) Therefore, we can evaluate the actual groundwater velocity by carrying out a similar experiment in the field and by applying the coefficient obtained from the field experiment to the relational expression.

3 T s [ºC] u g = 0, 265, 377, 833, 1383, 1963 m/year from top to bottom Heating rate from thermal probe:6.6 W/m Figure 1 Variations in temperature of thermal probe with ground water velocity k [K] k wf = e u g = 265, 377, 833, 1383, 1963 m/year from top to bottom k wf = e k = e k wf = e k wf = e Figure 2 Variations in temperature gradient with elapsed time 2500 u [m/year] u = 55884n E E E E-03 Figure 3 Relation between groundwater velocity and coefficient of gradient n Method of field experiment It is essential that the test object resembles a line heat source in order to be able to measure the actual groundwater velocities. Consider the three methods shown in Figure 4. In the first method, the thermal probe, which includes a temperature sensor and a heating element, is buried in the ground. In this method, the thermal probe must be secured to avoid displacement during the procedure. Additionally, since it is too difficult to bury the thermal probe deep in the ground, the process of boring, installing the thermal probe, and carrying out the experiment are carried out in steps. This method has an advantage that the experimental time per test can be minimized. Extremely small groundwater velocities of around 100 m/ year were accurately detected in the two-hour-long experiment. n

4 The second method involves boring an observation well and inserting a linear heater that can uniformly heat the observation well and temperature sensors that can measure the temperature distribution in the well. The experimental time per test is more than that in the case of the first method and the accuracy is inferior. The advantage of the method is that in addition to the groundwater velocity, the distribution of the velocity can be measured as well. The last method is called the long-term thermal response test (TRT). When TRT is carried out with a general borehole ground heat exchanger for several days or a few weeks, the groundwater flow influences the thermal response of the thermal medium in the ground heat exchanger. Using this method the effective influence of the groundwater velocity on the ground heat exchanger can be evaluated directly. Constant voltage device Data logging machine Constant voltage device Data logging machine TRT apparatus T T Data logging machine Boring rod Casing Temperature sensor Heater U-tube Thermal probe Borehole (well) (a) Probe method (b) Heating well method (c) Thermal response test Figure 4 Method of field experiment to evaluate groundwater velocity 3. PROBE CALIBRATION EXPERIMENT The probe calibration experiment, which is illustrated in Figure 5, was conducted in order to determine the groundwater velocity in the field experiment. A thermal probe is inserted in the sand layer of the calibration tank. Flow of water is enabled in the sand layer by maintaining a constant difference in the water levels of the second and fourth parts of the calibration tank. The simulated flow of water is maintained at a constant temperature by using the constant water temperature bath that is connected to the second part of the calibration tank. Figure 6 shows the cross-sectional view of the thermal probe. The probe is the same as the one used for the field experiment described in Section 4. The heater and Pt-100 sensor are sheathed in a stainless steel pipe of length 200 mm and external diameter 3.2 mm. In addition, secure the probe, it is inserted in a stainless steel pipe, whose external and internal diameters are 10.5 mm and 5.7 mm, respectively. In the experiment, the temperature of the thermal probe was measured under the condition of constant heat generation from the probe. The experimental conditions are listed in Table 1. The experiments were carried out by varying the velocity of the simulated groundwater flow. Figure 7 shows the temperature variations in the thermal probe with respect to the elapsed time and varying groundwater velocities. The variations in the temperature gradient, as calculated by Equation (1), are shown in Figure 8. The variations in temperature and temperature gradient were

5 similar to the ones described in Section 1. From this result, the authors obtained a relation between the measured groundwater velocity and the coefficient of gradient n in Figure 9. An approximate equation of the relation, which can be used in the field experiment, is as follows: u = n (4) Temperature measuring point (Thermocouples) Constant temperature bath Calibration tank Constant voltage device 1st 2nd 3rd 4th 5th Data logging machine Insulation material (Polystyrene : thickness mm) Thermal probe Figure 5 Schematic diagram of probe calibration experiment Stainless sheath pipe (External diameter: 10.5 mm, internal diameter: 5.7 mm) Stainless sheath pipe Temperature measuring point (Pt-100) Heating element Probe main frame To data logging machine Probe main frame including Pt-100 and heating element To constant voltage device Insert Figure 6 Cross-sectional view of thermal probe u g = 295, 0, 105, 711, 1470 m/year from top to bottom T [ o C] u g = 0, 105, 711, 295, 1470 m/year from top to bottom Heating rate from thermal probe: 4 W/m Figure 7 Probe temperature variations with varied ground water velocity k [K] Figure 8 Variations of temperature gradient

6 2000 u [m/year] u = n n Figure 9 Relation between groundwater velocity and coefficient of gradient n 4. FIELD EXPERIMENT Groundwater velocities under actual conditions were measured by using the same probe described in Chapter 3. The experimental site is the building where a GHSP system was installed utilizing steel foundation piles. The geological stratum of the experimental site and the experimental process are shown in Figure 10. The stratum mainly consists of gravel and sand and the groundwater level is 5.3 m. The probe is installed at 7 points indicated in Figure 10 and the experiment is carried out at those points. Thermal probe point 1 6 m 4 Boring rod Hummer (63.5kg) drop 2 1 m 1 m Casing 1 m 1 m Core tube 3 Thermal probe Probe for trephination ~1m surface soil ~4m silt and sand ~10m gravel and sand ~12m gravel and pebble Figure 10 Geologic stratum of the site and experimental process Figures 11 and 12 show the variations in the probe temperature and the temperature gradient as calculated by Equation (1), respectively. The temperature variation at a depth of 6 m varies linearly with the logarithmic elapsed time. Further, no variations in the temperature gradient are observed after 1000 s. This indicates that the groundwater flow is not generated at that point. Using these results and Equation (4), the groundwater velocities at each point were determined.

7 Figure 13 shows the calculated groundwater velocities. The groundwater velocities estimated using the conventional method are also shown in Figure 13. The groundwater velocities obtained by the probe method are 0 m/year at a depth of 6 m and 100~200 m/year at a depth of 7~10 m and they are almost equal to the values estimated by the conventional method at the same point. Thus, this method is effective to measure the groundwater velocity. T [ o C] Depth 6, 10, 8, 9, 7 m from top to bottom Heating rate from thermal probe: 4 W/m Figure 11 Probe temperature variations at various depths 10.0 Depth 6, 10, 8, 9, 7 m from top to bottom k [K] Figure 12 Variations in temperature gradient at various depths 0 2 Probe method Conventional method Depth [m] u [m/year]

8 Figure 13 Groundwater velocity evaluated by probe method and conventional method 5. CONCLUSION 1. A practical method for measuring groundwater velocity by measuring the gradient of thermal response was introduced. In addition, three types of field experiments, i.e., the thermal probe method, heating well method and thermal response test, were suggested. 2. A probe calibration experiment, which involves the used of a thermal probe and a calibration tank, was conducted in order to determine the groundwater velocity in the field experiment. As a result, an approximate equation that expresses the relation between groundwater velocity and coefficient n in the equation of temperature gradient was obtained. 3. A field experiment for measuring groundwater velocity with the same thermal probe as the one used in the calibration experiment was carried out. The groundwater velocities that were measured by using the temperature gradients in the field experiment and the approximate equation obtained in the calibration experiment were 0 m/year at a depth of 6 m and 100~200 m/year at a depth of 7~10 m. These values were close to the ones yielded by the conventional method at the same points. Thus, the thermal probe method is effective for measuring groundwater velocity. ACKNOWLEDGEMENT This work was supported by the technological development project Development of low flow circulation ground source heat pump multi-split system and its design and operation method (Project representative: Hiroyuki Takahashi of Nippon Steel Engineering) to prevent global warming as an initiative of the Ministry of Environment. In addition, we would like to express our gratitude to the Sapporo city government for providing us with the experimental site. NOMENCLATURES k: Temperature gradient [K], T: Temperature [ºC], t: Time [s], u: Groundwater velocity [m/s] REFERENCES Carslaw, H. S. and J. C. Jaeger: Conduction of Heat in Solids, Oxford University Press, 1959 Diao, N., L. Qinyun and F. Zhaohon: Heat Transfer in Ground Heat Exchangers with Groundwater Advection, International Journal of Thermal Sciences 43, pp , 2004 Katsura, T., K. Nagano, S. Takeda and K. Shimakura: Heat transfer experiment in the ground with groundwater advection, Proceedings of 10th Energy Conservation Thermal Energy Storage Conference Ecostock 2006, New Jersey,