Sound Speed in LiquidGas Mixtures: WaterAir and WaterSteam

The sound speed of a two-phase fluid, such as a magma-gas, water-air, or water-steam mixture, is dramatically different from the sound speed of either pure component. In numerous geologic situations the sound speed of such two-phase systems may be of interest: in the search for magma reservoirs, in seismic exploration of geothermal areas, in prediction of P wave velocity decreases prior to earthquakes, and in inversion of crustal and upper mantle seismic records. Probably most dramatically, fluid flow characteristics during eruptions of volcanoes and geysers are strongly dependent on the sound speed of erupting two-phase (or multiphase) fluids. In this paper the sound speeds of water, air, steam, water-air mixtures, and water-steam mixtures are calculated. It is demonstrated that sound speeds calculated from classical acoustic and fluid dynamics analyses agree with results obtained from finite amplitude 'vaporization wave' theory. To the extent that air and steam are represented as perfect gases with an adiabatic exponent •, independent of temperature, their sound speeds vary in a simple manner directly with the square root of the absolute temperature. The sound speed of pure liquid water is a complex function of pressure and temperature and is given here to 8 kbar, 900øC. In pure water at all pressures the sound speed attains a maximum value near 100øC and decreases at higher temperatures; at high pressures the decrease is continuous, but at pressures below 1 kbar the sound speed reaches a minimum value in the vicinity of 500ø-600øC, above which it again increases. The sound speed of a water-air mixture depends on the pressure, the void or mass fraction of air, the frequency of the sound wave, and, if surface tension effects are included, on bubble radius. The admixture of small volume fractions of air causes a dramatic lowering of the sound speed by nearly 3 orders of magnitude. The sound speeds of the pure liquid and gas end-members are nearly independent of pressure, but the sound speed of a mixture is highly dependent on pressure. Calculated values for water-air mixtures are in good agreement with measured values. The sound speed in a single-component two-phase system, such as a water-steam mixture, depends on whether or not equilibrium between the phases on the saturation curve is maintained. Heat and mass transfer which occur when equilibrium is maintained cause the sound speed to be much lower than under nonequilibrium conditions in which heat and mass transfer are absent. The sound speed in a water-steam mixture may be as low as I m s -x