Mathematical Modelling of Two-Phase Geothermal Systems

Abstract

This thesis investigates the formation of two-layer structures within geothermal systems by the use of mathematical modelling. A new conceptual and mathematical framework, which embodies the governing features of two-phase flows in porous media, is presented. Dimensional methods, linear stability theory, and numerical analysis are used. The formation of two-layer structures within homogeneous reservoirs is explained by quasi-static changes in the vertical heat flow, reservoir permeability, and total mass of water in the system. Our results show that steady-states with a distinct vertical two-layer structure develop from the same initial vapour-dominated steady-state, but in response to different geothermal processes: e.g., decrease or increase in the amount of heat transported to the base of a reservoir; decrease or increase in reservoir permeability; injection or withdrawal of fluid through reservoir boundaries. Thus, the formation of a water zone underlying a vapour-dominated region (Wairakei, NZ) can indicate that the system undergoes a process of slow cooling. A steam zone underlying a vapour-dominated region (The Geysers, CA) can be formed either as a result of slow heating or as a result of a reduction in permeability. A steady-state with an upper vapour-dominated part and a lower liquid-dominated part (Larderello, Italy) can occur if the permeability of the system has been gradually increased.