Pore fluid percolation and flow in ductile rocks
Ductile rocks have capacity to deform in response to large strains without macroscopic fracturing. Such behavior may occur in rocks that did not undergo diagenesis, in weak materials such as rock salt or at greater depths in all rock types where higher temperatures promote crystal plasticity and higher confining pressures suppress brittle fracture (partially molten rocks). The pore network topology and fluid distribution in ductile rocks are governed by textural equilibrium. Therefore, textural equilibrium controls the distribution of the liquid phase in many naturally occurring porous materials such as partially molten rocks and alloys, salt-brine and ice-water systems. In this dissertation, we present a level set method to compute an implicit representation of the liquid-solid interface in textural equilibrium with space-filling tessellations of multiple solid grains in three dimensions. In ductile rocks, pore geometry evolves to minimize the solid-liquid interfacial energy while maintaining a constant dihedral angle, θ, at solid-liquid contact lines. Interfacial energy minimization with level set method is achieved by evolving the solid-liquid interface under surface diffusion to constant mean curvature surface. The liquid volume and dihedral angle constraints are added to the formulation using virtual convective and normal velocity terms. This results in a initial value problem for a system of nonlinear coupled PDEs governing the evolution of the level sets for each grain. A domain decomposition scheme is devised to restrict the computational domain of each grain to few grid points around the grain. The coupling between the interfaces is achieved in a higher level on the original computational domain. Our results show that the grain boundaries with the smallest area can be fully wetted by the pore fluid even for θ > 0. This was previously not thought to be possible at textural equilibrium and reconciles the theory with experimental observations. Even small anisotropy in the fabric of the porous medium allows the wetting of these faces at very low porosities, ϕ < 3%. Percolation and orientation of the wetted faces relative to the anisotropy of the fabric are controlled by θ. We have studied the fluid percolation and percolation thresholds in regular and irregular media. The results show that the pore space is connected at any non-zero porosity when θ ≤ 60°, and percolation threshold in an irregular media comprised of grains with different shapes and sizes is much higher than previously thought. Our results show that the pore network connectivity in ductile rocks is affected by the history of the systems and hysteresis determines the percolation when θ > 60°. We have also computed permeability of the pore networks in different porosities and dihedral angles for both regular and irregular media using Lattice Boltzmann method. Furthermore, we studied the effects of grain texture anisotropy on the permeability anisotropy. Until recent years, rock salt has been considered to be impermeable as it seems to contains and keep gas inclusions for long time. Increasing energy demand and necessity of producing hydrocarbon reservoir enclosed or touched by salt deposit and also urgent need of safe repository sites for high-level nuclear waste have brought attention to research and study the porosity and permeability of natural rock salt. Rock salt in sedimentary basins has long been considered to be impermeable and provides a seal for hydrocarbon accumulations in geological structures. The low permeability of static rock salt is due to a percolation threshold. However, deformation may be able to overcome this threshold and allow fluid flow. We confirm the percolation threshold in static experiments on synthetic salt samples with X-ray microtomography. We then analyze wells penetrating salt deposits in the Gulf of Mexico. The observed hydrocarbon distributions in rock salt require that percolation occurred at porosities considerably below the static threshold, due to deformation-assisted percolation. In general, static percolation thresholds may not always limit fluid flow in deforming environments. Here we use pore-scale simulations of texturally equilibrated pore networks to study the possibility of core formation by porous flow in planetesimals. Rapid core formation in early planetary bodies is required by geochemical data from extinct radionuclides. The most obvious mechanism for metal-silicate differentiation is the segregation of dense core forming melts by porous flow. However, experimental observations show that the texturally equilibrated metallic melt resides in isolated pockets that prevent percolation towards the center. The proposed hypothesis in this dissertation is that the porosities can be large enough to exceed percolation threshold and allow metalic melt drainge to center. The melt network remains interconnected as drainage reduces the porosity below the percolation threshold and only 1-2% is trapped. X-ray microtomography of lodran-like meteorite NWA 2993 provides evidence that volume fraction of metallic phases can exceed this percolation threshold. Lattice Boltzmann simulations show that the permeability during drainage remains significant. A model for metal-silicate differentiation by porous flow in a viscously compacting planetesimal is also proposed and shows that the efficient core formation requires early accretion and is completed almost 2 Myr after the onset of melting.