Effect of Temperature-dependency of Thermal Properties on Heat Diffusion in Rock Around a Heat Storage Cavern

We analyzed the pattern of heat diffusion in rock around an underground heat storage cavern with considering temperature-dependency of thermal properties. Based on theoretical solutions of heat diffusion for a semi-infinite boundary (a linear variation form) and a circular boundary (a radial logarithmic variation form), a shape factor in heat diffusion equation for a horse-shoe shape cavern boundary is determined as a semi-radial variation form (square-root of logarithm). We analyzed heat diffusion patterns for various cases of thermal conductivities, specific heats and heat storage boundary conditions. A linear form of heat diffusion equation produced larger temperature gap than a semi-radial form and a radial form. The temperature gap caused by the variation of thermal conductivity is more sensitive than that by the variation of specific heat. We also derived the correlation equations and the variation range of maximum temperature gap for entire cases. The pattern for a semi-radial form lies between the patterns for a linear and a radial forms where a linear form is upper boundary and a radial form is lower boundary. These results can supplement the simplified analysis using constant thermal properties.