Dynamics and energetics of bubble growth in magmas: Analytical formulation and numerical modeling

We have developed a model of diffusive and decompressive growth of a bubble in a finite region of melt which accounts for the energetics of volatile degassing and melt deformation as well as the interactions between magmatic system parameters such as viscosity, volatile concentration, and diffusivity. On the basis of our formulation we constructed a numerical model of bubble growth in volcanic systems. We conducted a parametric study in which a saturated magma is instantaneously decompressed to one bar and the sensitivity of the system to variations in various parameters is examined. Variations of each of seven parameters over practical ranges of magmatic conditions can change bubble growth rates by 2–4 orders of magnitude. Our numerical formulation allows determination of the relative importance of each parameter controlling bubble growth for a given or evolving set of magmatic conditions. An analysis of the modeling results reveals that the commonly invoked parabolic law for bubble growth dynamics R∼t1/2 is not applicable to magma degassing at low pressures or high water oversaturation but that a logarithmic relationship R∼log(t) is more appropriate during active bubble growth under certain conditions. A second aspect of our study involved a constant decompression bubble growth model in which an initially saturated magma was subjected to a constant rate of decompression. Model results for degassing of initially water‐saturated rhyolitic magma with a constant decompression rate show that oversaturation at the vent depends on the initial depth of magma ascent. On the basis of decompression history, explosive eruptions of silicic magmas are expected for magmas rising from chambers deeper than 2 km for ascent rates \u3e1–5 m s−1

Reply [to “Comment on “Dynamics and energetics of bubble growth in magmas: Analytical formulation and numerical modeling” by A. A. Proussevitch and D. L. Sahagian”]

We have developed a model of diffusive and decompressive growth of a bubble in a finite region of melt which accounts for the energetics of volatile degassing and melt deformation as well as the interactions between magmatic system parameters such as viscosity, volatile concentration, and diffusivity. On the basis of our formulation we constructed a numerical model of bubble growth in volcanic systems. We conducted a parametric study in which a saturated magma is instantaneously decompressed to one bar and the sensitivity of the system to variations in various parameters is examined. Variations of each of seven parameters over practical ranges of magmatic conditions can change bubble growth rates by 2–4 orders of magnitude. Our numerical formulation allows determination of the relative importance of each parameter controlling bubble growth for a given or evolving set of magmatic conditions. An analysis of the modeling results reveals that the commonly invoked parabolic law for bubble growth dynamics R∼t1/2 is not applicable to magma degassing at low pressures or high water oversaturation but that a logarithmic relationship R∼log(t) is more appropriate during active bubble growth under certain conditions. A second aspect of our study involved a constant decompression bubble growth model in which an initially saturated magma was subjected to a constant rate of decompression. Model results for degassing of initially water‐saturated rhyolitic magma with a constant decompression rate show that oversaturation at the vent depends on the initial depth of magma ascent. On the basis of decompression history, explosive eruptions of silicic magmas are expected for magmas rising from chambers deeper than 2 km for ascent rates \u3e1–5 m s−1

Dynamics of coupled diffusive and decompressive bubble growth in magmatic systems

Bubble growth in an ascending parcel of magma is controlled both by diffusion of oversaturated volatiles and decompression as the magma rises. We have developed a numerical model which explores the processes involved in water exsolution from basaltic and rhyolitic melts rising at a constant rate from magma chamber depths of 4 and 1 km. While the model does not attempt to simulate natural eruptions, it sheds light on the processes which control eruptive behavior under various conditions. Ascent rates are defined such that a constant rate of decompression dP/dt is maintained. A variety of initial ascent rates are considered in the model, from 1 m/s to 100 m/s for basalts, and from a few centimeters per second to 10 m/s for rhyolite, at the base of the conduit. The model results indicate that for any reasonable ascent rate, basaltic melt degasses at a rate sufficient to keep the dissolved volatile concentration at equilibrium with the decreasing ambient pressure. Rhyolitic melt reaches the surface at equilibrium if its ascent rate is less than 1 m/s, but it can erupt with high oversaturation at greater ascent rates. The latter may lead to explosive eruptions. If the ascent rate of rhyolite is 10 m/s or more, then melt barely degasses at all in the conduit and erupts with the highest oversaturation possible. For the case of slow magma rise, bubble growth is limited by decompression. For the case of rapid magma rise, bubble growth is limited by diffusion. The results of our simple model do not accurately simulate natural volcanic eruptions, but suggest that subsequent, more complex models may be able to simulate eruptions using the insights regarding diffusive and decompressive bubble growth processes explored in this study. Numerical modeling of volcanic degassing may eventually lead to better prediction of eruption timing, energetics and hazards of active volcanoes