PHYSICAL MODELS OF FUMAROLIC FLOW

Transport of gas from subsurface magma to the atmosphere is modelled as flow through a narrow, rough pipe, and through a wider conduit filled with spheres, representing flow in a porous pipe. Macroscopic mass, momentum and energy balances are written for a control volume representing a short vertical section of the pipe. The balances are solved for a perfect gas with the approximate thermodynamic properties of steam, losing heat by steady-state radial conduction through the pipe walls, with boundary conditions of magmatic temperature at the base of the pipe, atmospheric pressure at the surface, and an ambient geotherm at a specified distance from the conduit. Results yield the variation of exit temperature with magmatic source depth, conduit radius, mass flow rate per unit area, distance to ambient temperatures, vent porosity, and porous particle size. Two ambient geotherms are used: (1) a linear gradient from atmospheric to magmatic temperatures; and (2) a 'hydrothermal' geotherm, based on water saturation temperatures assuming a hydrostatic pressure gradient. Because individual vents commonly cluster, the porous pipe model is considered to be more realistic than the rough pipe model, mainly because the conductive cooling approximation is more likely to remain valid. Exit temperatures fall as conductive losses increase, i.e. as the source depth increases, the conduit narrows, the mass flow decreases, the distance to ambient temperatures reduces, or the ambient geotherm cools. The porous pipe model is applied to data from two fumarole fields, and indicates magmatic source depths of < 100 m for the approximately 900-degrees-C fumaroles present at Poas in 1982, and < 1 500 m for the approximately 300-degrees-C field at Vulcano during 1983-87. Because additional cooling mechanisms, such as hydrothermal circulation in the country rock and addition of cool hydrothermal fluid to the gas, are likely to occur, these calculated depths to magma are maxima. Calculated pressures at the base of conduits are typically near atmospheric, indicating that the majority of decompression from magmatic pressures occurs immediately as the gas escapes. Escape is thought to be best approximated as a Joule-Kelvin expansion, and has negligible affect on gas temperature. Low pressures throughout the conduit may have important implications for equilibrium pressures calculated from exit chemical compositions, and will encourage invasion of hydrothermal fluids with time. Small changes in atmospheric pressure will affect the pressure differential across the magma boundary, and hence may influence the degassing rate, mass flow, and exit temperature.