Fluid flow and damage in two-phase media: Theory and applications to magma and environmental dynamics

Two-phase flows exist in many processes in the Earth over disparate time scales. Damage (void generation and micro-cracking) in the flow are relevant for geological processes such as magma-fracturing during melt migration through the upper mantle on the geological time scale, and hydro-fracturing of crustal rocks during subsurface fluid injection on the human time scale. This dissertation is devoted to the theoretical and numerical study of damage, deformation, and fluid flow in porous rocks as a coupled process. Mathematical models are developed for coupled fluid transport in both viscous and poro-elastic rocks, and help us to explain the weakening and fracturing mechanisms within the two-phase flow in deformable porous rocks. Two damage problems are constrained and discussed with the developed model: 1. During magma migration, what is the mechanism of the transition from a magmatic porous flow originated in the viscous asthenosphere to fracture propagation in the elastic lithosphere? 2. During the subsurface fluid injection, how does damage weaken the strength of the rock matrix and affect the diffusion and distribution profiles of porosity and overpressure? In Chapter 2 I employ two-phase physics and interface thermodynamics to describe void/microcrack formation. The transition from porous flow to fracturing is described by a nonequilibrium relation between interfacial surface energy, pressure and viscous deformation. I study the effect of pore-generating damage on the propagation of both steady-state fluid flow and time-dependent porosity waves, and show that damage enhances melt migration by causing focused porosity and faster migration. In Chapter 3 I extend the 1-D model in Chapter 2 into two-dimensional space, and study the formation of finite-amplitude, two-dimensional magmatic solitary waves with and without solenoidal (rotational) flow of the matrix. The change in geometry of stably propagating circular waves indicates a transition from' magmatic porous flow to dike-like magma-fracturing as magma passes through a semibrittle/semi-ductile zone in the lithosphere. In Chapter 3 I develop a two-phase viscoelastic damage model and provide a basic framework to study the pressure and porosity diffusion in fractured near-surface porous rocks. The model shows that while nonlinear permeability models result in an enhanced diffusivity, damage makes the matrix more compressible. The net effect is that the porosity diffusivity is reduced causing fluid infiltration to accumulate closer to the injection source, leading to a slower fluid diffusion during hydro-fracturing with a fixed porosity boundary condition. However if a constant over-pressure boundary condition is applied, a weakened matrix with damage leads to greater pressure diffusivity than for porosity.