Pressure evolution during the recharge of a bubbly magma reservoir

Pressurization of magma reservoirs through the recharge of fresh magma is an important process in magmatic systems and has been associated with pre-eruptive ground deformation, eruption triggers and effusive/extrusive eruption styles. Long-lived shallow magma reservoirs may contain an exsolved volatile gas phase in the form of bubbles suspended in incompressible melt making the magma compressible. Bubbles could mitigate pressurization through their compressibility, and by resorbing volatiles. In this study, we use numerical models to investigate the effect of magma compressibility added by a soluble gas bubble phase, and to calculate the pressure response of a bubbly magma under a known recharge rate. I investigate this in three stages. Firstly, I use a simplified ‘toy model’ to understand the fundamental processes of a compressing gas-liquid system in a simple one dimensional piston geometry. Secondly, I adapt the model to calculate the pressure evolution of a spherical bubble surrounded by an incompressible melt shell and quantify the relative contributions of the gas pressure, surface tension acting on the bubble and viscous resistance from the melt shell toward the overall magma pressure as the sum of the 3 components. Finally, I adapt the model to investigate the pressure response of a bubbly magma body under a magma injection event. To ensure consistency with the previous two scenarios, I assume the end-member scenario of rigid reservoir walls and no magma mixing, so that the change in volume must be accommodated by a reduction in the volume of the pre-existing bubbles. Across all three stages, I find that the pressure evolution of the gas is dependent on the rate at which the gas can be resorbed. The pressure evolution can be described by a dimensionless Peclet number (�� = �� ⁄ �� ), which captures the ratio of the compression timescale �� and the diffusive timescale ��. We first consider two end members: 1) a no diffusive flux regime (�� ≪ 1) in which all the gas molecules remain in the bubble and the volume change is entirely accommodated by compression of the gas according to its equation-of-state (i.e. the gas is treated as insoluble); and 2) an equilibrium regime (�� ≫ 1) in which diffusion and resorption occur at perfect equilibrium with evolving pressure. Regime (1) constitutes the maximum rate of pressure increase, and regime (2) the minimum rate of pressure increase, for a given recharge rate. Furthermore, we find that the effects of surface tension and viscous resistance play a negligible role in the pressure evolution of large-scale natural magmatic systems undergoing recharge, therefore, we can reasonably assume that the gas pressure reflects the overall pressure of the magma. 7 However, viscosity and surface tension may be important factors for smaller systems such as laboratory experiments with high viscosity, low volume magmas. Finally, we find that, for natural estimates for bubble-bearing reservoirs under geological constraints of volume and injection rate, �� is consistently well within the equilibrium regime (�� ≫ 1). The system exhibits disequilibrium behaviour (�� ≤ 1) only under extreme conditions, which are highly unlikely in nature. We conclude that models of pressure evolution in a recharging magma reservoir are justified in using the simpler equilibrium model, for which an implicit analytical solution is provided.