Comparative Analysis of Fluid-Rock Dynamic Interaction Models

Abstract:

We examine the implicit dynamics in models of the fluid-rock interaction that may be occurring in magmatic conduits (e.g. Julian, 1994; Balmforth et al., 2005; Corona-Romero et al., 2012). We analyze and discuss major differences in their governing equations and geometry, and in their properties and parametric dependences. The models consider the fluid-rock dynamic interaction in a fluid driven conduit embedded in a solid elastic space. The formulations vary from 1D to 3D although the later is axisymmetric. The fluid and solid are dynamically coupled fulfilling continuity of normal velocities and stresses at the conduit's wall. A pressure transient at a point of the conduit, that perturbs a steady flow of incompressible viscous fluid, produces the interaction between the fluid and motion at the conduit's walls. The fluid motion induces the elastic response of the conduit wall forcing it to oscillate. This fluid-rock interaction may generate long lasting response. As a source, we used different pressure excitations functions (e.g. Dirac’s Delta, Gaussian function) including those measuring during simulations gas burst and fragmentation of volcanic rocks under controlled laboratory conditions. Changes in the source magnitude confirm the non-linear behavior of the fluid-rock interaction and the effects of the fluid properties as its viscosity. In our investigation the most robust approach (Corona-Romero et al., 2012) includes the analytical solution and allows changes in the properties of the fluid and the surrounding rock, and in the geometry, by coupling two or more conduits. Besides, the governing equations include the calculation of the pressure and the fluid history along the conduit as well as the velocity of the walls. Furthermore, the synthetics are comparable with those obtained experimentally. Our analyses explore the capabilities, advantages and limitations of the models to simulate volcanic seismic signals.