Sphere models for pore geometry and fluid permeability in heterogeneous magmas

The permeability of magmas to percolating fluids plays a role in controlling eruption explosivity. While measurements of volcanic rock permeability abound, comparison of these values with models that relate hydraulic properties to random heterogeneous pore structures are few. Here, we present such a comparison. First, we generate numerical materials composed of randomly placed spherical objects in a periodic control volume using two dominant pore structure families: (1) where the space between the spherical objects represents the pore phase that can transmit fluid, and (2) where the spherical objects themselves are the pore phase that can transmit fluid. In the former case, we envisage the system to be analogous to initially granular magmas that undergo welding events that serve to progressively reduce the porosity. In the latter case, we envisage the system to be analogous to vesiculating magmas that evolve to high porosities. In both cases, we constrain relationships for fundamental structural parameters for every porosity including the specific surface area and the percolation thresholds and we compare these with theoretical relationships. Importantly, we run lattice Boltzmann method simulations of fluid flow through these systems at a wide range of porosities to constrain the steady state Darcian fluid permeability using the LBflow code. We finally compare these permeability values with (1) other published simulations, (2) published permeability data for natural volcanic rocks or experimental analogues thereof, and (3) theoretical constraints derived from first principles. In all cases, we obtain a good agreement between our idealized numerical random systems and the natural data, as well as results of other theoretical and experimental approaches. We propose that the simple models that we derive and validate can be of wide utility in building more complex models for the evolution of magmas during shallow ascent with broad implications for outgassing efficiency and the development of pore overpressure immediately prior to eruption.