Computer simulation of time-dependent magma ascent processes involving bubbly and gassy flows

Abstract

Time-dependent magma ascent processes were analyzed using a computer simulation of bubbly and gassy (gas-particle dispersion) magma flows in a vertical conduit connected at its bottom to a magma chamber having finite capacity. Volatile elements in the bubbly flow were assumed to escape from the magma through lateral permeable gas flow driven by the pressure gradient originating from viscous resistance to the ascent velocity-dependent expansion of bubbles. The bubbly flow was assumed to fragment and to transform into a gassy flow when its gas volume fraction exceeded a critical value. Based on the simulation, an eruption is predicted to be explosive or effusive when a dimensionless degassing factor, which is proportional to the permeability and viscosity of the magma, is smaller or greater than a critical value, respectively. The state of gassy flow was calculated from the mass and momentum conservations that are met quasi-statically with continuities of mass flux and pressure at the interface with the underlying bubbly flow. The inertia force and an effective wall friction were considered as resistive forces working on the gassy flow. Some of the results of the simulation are shown to be consistent with observations of some recent eruptions. An effusive or explosive eruption is predicted to have relatively high activity with large exit velocities at its initial stage. The initial high activity is particularly significant for explosive eruptions that involve the rapid growth of a gassy flow zone. Explosive eruptions are shown to involve more efficient magma transport with higher mass flow rates than effusive eruptions, as has been predicted by some previous analyses of stationary magma flow. The efficient magma transport of explosive eruptions is associated with a peculiar pressure distribution consisting of gentler and steeper pressure gradients in the gassy and bubbly flow zones, respectively. At the interface between bubbly and gassy flows, the pressure scaled by that at the conduit bottom was found to be nearly constant through time. This peculiar pressure distribution allows explosive eruptions to be fed with more magma than has been stored in excess of the lithostatic balance. This mechanism can produce such anomalously low pressure in the chamber that significant surface subsidence and caldera formation may result.