An analytical method to determine rock spallation temperature and degree of heterogeneity in thermal spallation drilling for geothermal energy

Thermal spallation drilling is an alternative technology expected to be suitable for exploitation of geothermal energy in hard, polycrystalline rocks. The rock spallation temperature and degree of heterogeneity are two important parameters for spallation studies. The rock spallation temperature can offer guidance to provide a suitable temperature environment for different formations, and the degree of heterogeneity plays an important role in determining the spallability of rock. However, it is difficult to measure the rock's surface temperature at the onset of initial spallation and there is no universal method to determine the degree of heterogeneity of rock. This paper intends to provide a convenient analytical approach to approximate the rock spallation temperature and degree of heterogeneity for field applications. Based on the Weibull statistical theory of tensile failure, the rock temperature at spallation can be obtained by solving a set of over-determined equations. All other rock properties can be calculated based on the temperature, and then the degree of heterogeneity of rock can be determined. Compared with experimental data, the calculated rock spallation temperature and degree of heterogeneity are all within acceptable ranges. All results in this paper can provide implications for further study on thermal spallation drilling in geothermal reservoirs.