Modelling the Development of Natural Hydrothermal Eruptions

Abstract

This paper continues and consolidates earlier work (McKibbin, 1989, 1990) on preliminary modelling of hydrothermal eruptionswhich concentrated on modelling theundergroundprocess. The fundamental equations of motion and thermodynamics are solved in order to examine the properties of an expanding two-phase fluid rising vertically through porous rock and rock particles at the surface. The first models relied on a simple homogeneous Darcy's Law to calculate the pressure gradients underground. However, results showed that modifications are required. Here the effects of adding a non-linear (Forchheimer) term to the momentum equation are investigated. Numerical experiments reveal this term to be when rock permeabilities are relatively large. The motion of the twoboundaries,the "flashing front" and "erosionsurface", are examined here. The assumption (McKibbin, 1989) that the two frontsadvance downward at the samerate is modified here by using some results given in McKibbin (1990) which allow a separate estimate to be made of the "flashing front" speed. The distancebetween the two boundaries, which gives the thickness of the flashing zone, is found to increase with time; the "flashing front" moves faster than the eroding surface, whilst both are decelerating. Further work involving the effectsof cohesive rock stress is dealt with briefly.