Pore-Scale Geodynamical Modelling

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Many important geophysical and geological phenomena take place in fluid-filled porous rocks. Examples include the transport of melts in Earth's upper mantle below mid-ocean ridges and in magma chambers. Additionally, the presence of fluid phases affects the material properties of bulk rocks which in turn affect the measurements that we can use to investigate these systems - seismic velocity and electrical conductivity are both affected by fluid content. Geological porous media exhibit a very rich range of behavior. In Earth's upper mantle, on geological time scales, the solid matrix behaves like a very viscous liquid and so effects of compaction can occur where pores can be transported through the system. In "mushy layers", the fluid and solid phases can be exchanged through solidification and melting which can affect the buoyancy of the fluid and the permeability of the matrix. When seismic waves pass through fluid filled rocks, the fluids and solid matrix exert forces on one another that affect the propagation of these waves. Because of the complexity of pores and the extent of porous systems, it is common to treat these systems on a continuum level - individual pores are not resolved and the porosity is treated as a field in averaged equations. Examples of these equations include the compaction equations used to describe porous systems with ductile matrices and Biot's equations used to describe poro-elastic systems. These systems of equations are widely used in diverse fields of geophysics and engineering. However, there are many assumptions made in their derivations that have not been rigorously tested. In recent years, the field of "digital rock properties" has emerged in which pore scale imagery of real rocks is used as a modeling domain in a numerical simulation in which the behavior of fluids is calculated at the pore scale. If a sufficiently large simulation domain is used, these calculations can be used to calculate effective properties of porous systems. These calculations also have the advantage of elucidating the basic pore-scale mechanisms. In this proposal, I describe a course of research in which my group and I will use the continuum-scale porous medium equations to investigate novel effects that are relevant to the earth and use pore scale modeling to test continuum-scale theories and to determine effective material properties. In particular, I will be using pore-scale simulations to determine poorly constrained coefficients in Biot's equations describing poro-elasticity. I also propose to test many of the poorly constrained assumptions regarding compaction theory. Since the solid matrix is deformable in these cases, I will use advanced numerical methods that allow for a deforming simulation geometry. These will be the first ever pore scale simulations of compaction systems which will be used to test these equations and determine effective properties which will increase our understanding of these important earth materials.