Modelling Geothermal History

Abstract

This paper focuses on the application of two mathematical techniques, dimensional analysis and linear stability theory, to modelling the evolution of geothermal systems at geological time scales. Dimensional analysis is used to verify conceptual models and to identify key physical processes that lead to the development of various steady states. Linear stability theory is applied to explain how one steady state transforms into another. We discuss three most significant non-dimensional numbers for geothermal modelling: the Reynolds number, the Rayleigh number and dimensionless heat flux. The Reynolds and Rayleigh numbers are important for all sub-surface water flow problems, whereas dimensionless heat flux is particularly useful for modelling two-phase water-steam systems. The whole approach is based on appreciation of the time-varying nature of a geothermal system. A numerical example is presented.