SO₂ flux and the thermal power of volcanic eruptions

A description of the dynamics, chemistry and energetics governing a volcanic system can be greatly simplified if the expansion of magmatic gas can be assumed to be adiabatic as it rises towards the surface. The conditions under which this assumption is valid are clarified by analysis of the transfer of thermal energy into the low conductivity wallrocks traversed by fractures and vents from a gas phase expanding over a range of mass flux rates. Adiabatic behavior is predicted to be approached typically within a month after perturbations in the release of source gas have stabilized, this timescale being dependent upon only the characteristic length scale on which the host rock is fractured and the thermal diffusivity of the rock. This analysis then enables the thermal energy transport due to gas release from volcanoes to be evaluated using observations of SO₂ flux with reference values for the H₂O:SO₂ ratio of volcanic gas mixtures discharging through high temperature fumaroles in arc and mantle-related volcanic systems. Thermal power estimates for gas discharge are 10^1.8 to 10^4.1 MW_H during quiescent, continuous degassing of arc volcanoes and 10^3.7 to 10^7.3 MW_H for their eruptive stages, the higher value being the Plinean Pinatubo eruption in 1991. Fewer data are available for quiescent stage mantle-related volcanoes (Kilauea 10^2.1 MW_H) but for eruptive events power estimates range from 10^2.8 MW_H to 10^5.5 MW_H. These estimates of thermal power and mass of gas discharges are commensurate with power estimates based on the total mass of gas ejected during eruptions. The sustained discharge of volcanic gas during quiescent and short-lived eruptive stages can be related to the hydrodynamic structure of volcanic systems with large scale gaseous mass transfer from deep in the crust coupled with episodes of high level intrusive activity and gas release.