Mathematical modelling of fractures, silica deposition and thermoelasticity in hydrothermal upflow zones
The permeability of the fractured geothermal systems in the Taupo Volcanic Zone (TVZ) of New Zealand is continually evolving due to mineral deposition and stress transients. It is generally accepted that a cyclic process, involving mineral deposition and crack dilation, is responsible for the formation of mineral veins of up to a metre in thickness. Studies of vein formation have focussed on the mechanics of dilation. Seismic activity and hydrofracturing are commonly accepted as mechanisms that generate the stress transients required to cause refracturing. By contrast, thermal stress transients generated during the mineral deposition process have received very little attention. In this thesis we construct and analyse mathematical models to investigate aspects of possible thermo-fracturing quartz vein formation processes. A first model is presented for thermally driven flow in a homogeneous porous medium. Approximate steady state analytical solutions are obtained for the flow resulting from point and line heat sources using similarity methods and asymptotic analysis for different permeability structures representing the extreme cases of very small and very large crack spacing. These solutions are used as the basis to perform a detailed study, in a simple geometry, of the transient process of a single fracture, within the porous medium, healing by silica deposition. Solutions are obtained using analytical and numerical techniques. It is shown that the resulting temperature variations in the plume are always small and depend on the thickness and profile of the initial fracture aperture. Using the ideas and insight obtained, a simplified model is constructed for a radially fractured upflow zone which incorporates the thermally driven flow, silica deposition and thermal stress effects. It is shown that a temperature change of as little as 10°C in the upflow zone is sufficient to generate lithostatic size stresses in the upper kilometre of the hydrothermal system. A numerical solution is obtained using asymptotic analysis for the case of a large number of small individual fractures. The solution indicates that thermal stresses can act to enhance fracture permeability in upflow zones. The results of the modelling indicate that the permeability structure in a geothermal system has considerable affect on the distribution of temperature variations in the plume. For a large crack spacing the temperature variations in the upflow zones of geothermal systems are confined to a region with sharp outer boundary. The results also show that the effect of silica deposition in fractured geothermal systems depends highly on the permeability structure. Silica deposition resulting in large fractures within a smaller scale fracture system produces only small changes in plume temperature, whilst silica deposition in large fractures in a less permeable rock mass can cause 'choking' of the flow and hence large changes in flow paths and temperatures in the plume.