Thermal convection of temperature-dependent viscous fluids within three-dimensional faulted geothermal systems: Estimation from linear and numerical analyses

Linear stability analysis and numerical simulations of density-driven flow are presented in order to estimate the effects of temperature-dependent fluid viscosity variation on the onset of free thermal convection within a three-dimensional fault embedded into impermeable rocks. The strongly coupled equations of density-driven flow are linearized. The solution was obtained through expansion into Fourier series. Simple polynomial expressions fitting the neutral stability curves are given for a range of fault aspect ratios, fluid viscosity properties, and thermal conductivity heterogeneity, providing a new tool for the estimation of critical Rayleigh numbers in faulted systems. The results are validated against the limiting case of temperature-invariant viscosity (i.e., constant). 3-D numerical simulations of free convection within a fault are run using the finite element technique in order to verify the theoretical results. It turned out that at average geothermal temperature conditions, thermal convection can develop within faults which permeability is up to 4 times lower than the case of a fluid with constant viscosity, in agreement with the developed linear theory. The polynomial expressions of this study can be applied to any numerical model for testing the feasibility of fault convection in 3-D geothermal basin.