ESTIMATION OF EFFECTIVE THERMAL CONDUCTIVITIES ACCORDING TO MULTI-LAYERS BY THERMAL RESPONSE TEST WITH A SET OF FIBER OPTICS IN A U-TUBE

 This study improves thermal response test (TRT) by using a set of fiber-optic distributed temperature sensors (DTSs) to estimate effective thermal conductivities in multi-layered formations. These sensors are installed into both inlet and outlet pipes (a U-tube) to obtain vertical profiles of heat transfer fluid temperature at TRT in more detail than those obtained by single DTS as in previous studies. When the borehole is constructed in a formation with several horizontally layers, this study analyzes the effective thermal conductivity in each layer under the assumption of line heat source. In the analysis, the slopes of fluid temperature on logarithmic elapse time are averaged within each layer, and heat exchange rate is calculated using a sum of linear slopes of temperature with depth in both inlet and outlet pipes. Offset and averaging span for DTS calibration are evaluated by laboratory sink tests at constant temperatures. Finally, an example of the proposed method at Asahikawa City, Hokkaido, Japan, is shown. In the example, the formation consists of three layers; unconsolidated gravel, clay, and pre-Quaternary shale. The solutions of the effective thermal conductivity in each layer are converged commonly when the thicknesses for analysis are larger than 20 meters. The conductivity in the upper-gravelly layer is about 1.5 times larger than those in the mid-clayey and lower-shale layers, probably due to groundwater flow advection. The thickness-weighted average of conductivities in the three layers is almost equal to the conductivity by conventional TRT with Pt100 sensors. The solutions are also valid in terms of total heat exchange rate. In addition, a series of effective thermal conductivities is invariable among the cases of DTS data: 1) calibrated in the heating period, 2) smoothed additionally by the FFT low-pass filter, 3) randomly sampled as the boot-strap method, and 4) calibrated in the recovery period.