A closed-form solution for the horizontally aligned thermal-porous spheroidal inclusion in a half-space and its applications in geothermal reservoirs

Abstract

The inclusion model for pore pressure and near surface localized heating may be of practical importance to many geological applications including geothermal reservoirs and volcanoes. In literature, the axisymmetric inclusion problems considering vertically placed spheroidal inclusions have been examined, while the complementary problems concerning horizontal spheroidal inclusion have not drawn much attention. The latter lacks axial symmetry, and usually cannot be handled by the analytical methods developed for the symmetric case. The current work analytically explores this asymmetric problem of thermo-porous spheroidal inclusion with the assistance of geometric interpretation. The complete solution to the displacement, strain and stress is formulated in Cartesian coordinates for ease of engineering applications. The formulae are derived in compact closed-form expressions in terms of elementary functions, which are handy for analytical manipulations and computer programming. Furthermore, applications in geostructures are discussed, and benchmark examples are provided to validate the present solution.