Preliminary Analytical Solutions of the Geomechanical and Thermal Stresses on Fracture Walls

Geothermal energy exploration is heavily dependent on the findings of geophysical surveys and other exploratory methods that yield insight into subsurface characteristics of potential geothermal reservoirs, such as rock morphology, fault lining, and fluid dynamics. Thermal processes not only affect plate tectonics and activities along plate margins but are also responsible for density contrast and changes in rheology. Geothermal systems within the crustal region may appear as liquid- or vapor- dominated systems, as the physics of the water-rock interactions greatly differ from these geological settings. Building on the understanding of the parallel plate concept, Newtonian fluid flow is described within this system, hence generating a parabolic velocity profile, as this is readily used to capture the understanding of rheology within the crust. However, by considering the geometry of a fracture to be a long thick walled cylinder with axially restrained ends, the paper then seeks to investigate the effect of thermal strains attributed from the geothermal fluids towards the walls of the fracture. Furthermore, using a general problem or otherwise known as the Lam ́ problem, which introduces the radial, tangential and axial stresses, and the Hooke‟s law equations that relates the strains and stresses are modified to accommodate this thermal expansion. Using relevant mathematical approximations, analytical solutions for the respective second order differential equations are obtained and plotted. In addition, using appropriate COMSOL Multiphysics 4.2a modules the deformation of the fracture walls can be modeled.