A case for ground thermal conductivity through indicator kriging across the land of Japan
Ground thermal conductivity provides useful geologic information for thermal science and engineering researchers as it influences the individual conductivity of each type of rock or soil. The individual conductivities of various geological materials have been extensively researched to provide more insights into their variation with ground thermal conductivities at different target locations and depths. The design of borehole heat exchangers (BHEs) represents one key practical application of thermal heat conductivity for heat transfer analysis. Ground source heat pump (GSHP) systems are used in various applications like melting snow and cooling and heating buildings. They are flexible, stable, efficient, and can reduce carbon dioxide emission than conventional systems like gas boilers.
Typically, GSHP systems require one or multiple heat exchangers to extract the underground heat demand information. Today, most ground heat exchangers comprise of single or multiple u-tubes installed in the boreholes. This can be attributed to their advantages, including flexibility to accommodate increasing heat demand, and they can be installed in limited areas with high building density. The overall installation cost of GSHP systems depends on the required length of the BHE, heat pump performance, and the geological property of the area: thermal conductivity, heat capacity, and temperature. Unfortunately, accurate determination of the ground thermal conductivity has remained a big challenge due to the limited drilling data. Additionally, research on the large-scale three-dimensional (3D) distribution of ground thermal conductivities and the contribution of vertical profiles on the design and optimization of BHE is limited.
To this end, Hokkaido University researchers: Professor Yoshitaka Sakata, Professor Takao Katsura and Professor Katsunori Nagano developed a new probability-concept method based on the indicator kriging to estimate the ground thermal conductivity by interpolating the soil/rock thicknesses. The ground thermal conductivity was determined as a probability-weighted average of the individual rock/soil conductivities, estimated from the surrounding borehole data. The work is currently published in the journal, Geothermics.
In brief, both core-sampling and non-core sampling data were utilized. Eight rock/soil types were defined for the indicator kriging. The estimations were conducted over 5m vertical intervals and 200m depth in 0.5km regular cells found on a vast Japanese land with 46 thousand borehole data to establish the relationship between thermal conductivity and soil/rock types. The method was used in the nation-scale application and analysis of various vertical profiles in Japan. Also discussed in detail were the influence of topography on the ground thermal conductivity and modeling of vertical profiles for practical use.
Results showed that the ground thermal conductivity obtained from the individual thermal conductivities of the soil/rock types agreed well with those of the in-situ measurements. The kriging covered 67% of the total Japanese land. Examples of estimated thermal conductivities were demonstrated in the Kanto area at different depths: 50m, 100m, 150m and 200m. The ground thermal conductivities were less than 2 Wm-1K-1 for lowlands and terraces and 2.5 Wm-1K-1 for hills and mountains, which increased vertically with the increase in the depth. Notably, a sudden change in the ground thermal conductivity, attributed to geological complexity, was observed amongst the adjacent cells.
In summary, a probability-weighted average method for determining the ground thermal conductivity was reported. Compared with the other deterministic methods, the indicator kriging procedure considered the uncertainties in borehole data, ensuring accurate interpolation of the categorical variables. The relationship between thermal conductivities and soil/rock types with the topographical categories was depicted in the local maps of the Kanto area. The regression analysis of the vertical curves showed a vertical increase of the ground thermal conductivity of topographical categories, with the vertical profiles of each location exhibiting logarithmic curves without peaks. Professor Yoshitaka Sakata explained the new method presented a promising solution for accurate estimation of the ground thermal conductivity and can advance the design and planning of geothermal energy utilization.
Sakata, Y., Katsura, T., & Nagano, K. (2020). Estimation of ground thermal conductivity through indicator kriging: Nation-scale application and vertical profile analysis in Japan. Geothermics, 88, 101881.