Permeability as a toggle switch in fluid-controlled crustal processes

摘要

Fluid transport in the earth's crust is either extremely rapid, or extremely slow. Cracks, dikes and joints represent the former while tight crystalline rocks and impermeable fault gouge/seals represent the latter. In many cases, the local permeability can change instantaneously from one extreme to the other. Instantaneous permeability changes can occur when pore pressures increase to a level sufficient to induce hydro-fracture, or when slip during an earthquake ruptures a high fluid pressure compartment within a fault zone. This 'toggle switch' permeability suggests that modeling approaches that assume homogeneous permeability through the whole system may not capture the real processes occurring. An alternative approach to understanding permeability evolution, and modeling fluid pressure-controlled processes, involves using local permeability rules to govern the fluid pressure evolution of the system. Here we present a model based on the assumption that permeability is zero when a cell is below some failure condition, and very large locally (e.g. nearest neighbors) when the failure condition is met. This toggle switch permeability assumption is incorporated into a cellular automaton model driven by an internal fluid source. Fluid pressure increases (i.e. from porosity reduction, dehydration, partial melt) induce a local hydro-fracture that creates an internally connected network affecting only the regions in the immediate neighborhood. The evolution, growth, and coalescence of this internal network then determines how fluid ultimately flows out of the system when an external (drained) boundary is breached. We show how the fluid pressure state evolves in the system, and how networks of equal pore pressure link on approach to a critical state. We find that the linking of subnetworks marks the percolation threshold and the onset of a correlation length in the model. Statistical distributions of cluster sizes show power law statistics with an exponential tail at the percolation threshold, and power laws when the system is at a critical state. The model provides insights into mechanisms that can establish long-range correlations in flow networks, with applications to earthquake mechanics, dehydration, and melting.