Mathematical modelling of underground flow processes in hydrothermal eruptions : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Palmerston North, New Zealand

Abstract

This thesis reports on a study of underground fluid flow and boiling processes which take place in hydrothermal eruptions. A conceptual model is presented for the eruptive process and a laboratory scale physical model confirming the effectiveness of this process is described. A mathematical formulation of the underground flow problem is given for two fluid flow regimes: two-phase homogeneous mixture (HM) flow and separable two-phase (SP) flow. Solutions to the system of equations obtained are solved under the simplifying assumptions of two-dimensional steady isothermal flow and transient non-isothermal horizontal flow. The main contribution of the study on steady isothermal flows is a description of how the ground flow may recover following a hydrothermal eruption. A numerical technique developed for plotting the streamlines in this case (and verified against analytic results) may also have applications in solving the steady non-isothermal flow problem. The main contribution of the study on the transient horizontal flow problem is a comparison of the differing predictions of HM and SP flow. The rate at which a boiling front progresses through a porous medium and the degree of boiling which occurs is described for each fluid flow regime. A set of horizontal physical experiments and numerical simulations have also been carried out for comparison with the mathematical model. Qualitative results for these three models agree. Suggestions given for improvements to the design of the physical experiment provide a basis for future study into the type of flow which occurs in hydrothermal eruptions