Nonequilibrium flow in volcanic conduits and application to the eruptions of Mt. St. Helens on May 18, 1980, and Vesuvius in AD 79

Abstract

A steady-state, one-dimensional, and nonhomogeneous two-phase flow model was developed for the prediction of local flow properties in volcanic conduits. The model incorporates the effects of relative velocity between the phases and for the variable magma viscosity. The resulting set of nonlinear differential equations was solved by a stiff numerical solver and the results were verified with the results of basaltic fissure eruptions obtained by a homogeneous two-phase flow model, before applying the model to the eruptions of Mt. St. Helens and Vesuvius volcanoes. This verification, and a study of the sensitivity of several modeling parameters, proved effective in establishing the confidence in the predicted nonequilibrium results of flow distribution in the conduits when the mass flow rate is critical or maximum. The application of the model to the plinian eruptions of Mt. St. Helens on May 18, 1980, and Vesuvius in AD 79, demonstrates the sensitivity of the magma discharge rate and distributions of pressure, volumetric fraction, and velocities of phases, on the hydrous magma viscosity feeding the volcanic conduits. Larger magma viscosities produce smaller mass discharge rates (or greater conduit diameters), smaller exit pressures, larger disequilibrium between the phases, and larger difference between the local lithostatic and fluid pressures in the conduit. This large pressure difference occurs when magma fragments and may cause a rupture of the conduit wall rocks, producing a closure of the conduit and cessation of the volcanic eruption, or water pouring into the conduit from underground aquifers leading to phreatomagmatic explosions. The motion of the magma fragmentation zone along a conduit during an eruption can be caused by the varying viscosity of magma feeding the volcanic conduit and may cause intermittent phreatomagmatic explosions during the plinian phases as different underground aquifers are activated at different depths. The variation of magma viscosity during the eruptions of Mt. St. Helens in 1980 and Vesuvius in AD 79 is normally associated with the tapping of magmas from different depths of the magma chambers. This variation of viscosity, which can include different crystal and dissolved water contents, can also produce conduit wall erosion, the onset and collapse of volcanic columns above the vent, and the onset and cessation of pyroclastic flows and surges.