Modeling of the ascent of magma during the plinian eruption of Vesuvius in A.D. 79

Abstract

The ascent of magma during the A.D. 79 eruption of Vesuvius was studied by a steady-state, one-dimensional, and nonequilibrium two-phase flow model. The gas exsolution process was modeled by assuming a chemical equilibrium between the exsolved and dissolved gas, whereas the magma density and viscosity were modeled by accounting for the crystal content in magma. The exsolution, density, and viscosity models consider the effect of different compositions of the white and gray magmas. By specifying the conduit geometry and magma composition, and employing the model to search for the maximum discharge rate of magma which is consistent with the specified geometry and magma composition, the model was then used to establish the two-phase flow parameters along the conduit. It was found that for all considered conditions the magma pressure in the conduit decreases below the lithostatic pressure near the magma fragmentation level, and that in the deep regions of the conduit the white magma pressure is larger and the gray magma pressure is lower than the lithostatic one. The exsolution and fragmentation levels were found to be deeper for the white than for the gray magma, and the changing composition during the eruption causes an increase of the exit pressure and decrease of the exit gas volumetric fraction. The model also predicted a minimum conduit diameter which is consistent with the white and gray magma compositions and mass flow-rates. The predictions of the model were shown to be consistent with column collapses during the gray eruption phase, large presence of carbonate lithics in the gray pumice fall deposit, and magma-water interaction during a late stage of the eruption.