A General Model for the Permeability of Magma Mush

Percolation through magma mush is a key transport mechanism for melts in the crust and is influenced by the permeability of the crystal framework. Existing models for mush permeability do not account for the range of microstructures that can evolve as mushes crystallize or compact to low melt fractions. Here, we use numerically generated domains of cuboids at the random maximum packing as a starting geometry for a loose magma mush. We then expand the cuboid edges into the pore spaces sequentially, representing a geometrical simulation of crystal overgrowth and crystallization. At each iterative step, we measure the melt fraction, specific surface area, and melt permeability via 3D fluid flow simulations. We find that (a) the permeability drops proportional to the drop in surface area as the melt fraction reduces, (b) the permeability falls to zero at a percolation threshold ${\varphi }_c=0.0187\pm 0.0010$ that is independent of scale and insensitive to the starting cuboid geometry, and (c) once the percolation threshold is determined, our data match a universal percolation model without requiring any free fitting parameters. We show how this percolation model accounts for any 3D shape of the crystals that comprise the evolving mush. Importantly, this approach demonstrates that mush permeability can remain non-zero in texturally unequilibrated mushes, down to very low melt fractions. Our model outperforms previous models, which overestimate mush permeability by up to three orders of magnitude, and our model can be used to accurately predict how mush permeability changes as mushes mature and crystallize, with implications for quantifying melt extraction, percolation rates, and melt reservoir assembly.