The importance of pore throats in controlling the permeability of magmatic foams

Foam formation during vesiculation of hydrous magmatic melts at 1 atm was studied in situ by synchrotron X-ray tomographic microscopy at the TOMCAT beamline of the Swiss Light Source (Villigen, Switzerland). Four different compositions were studied; basaltic, andesitic, trachyandesitic and dacitic hydrous glasses were synthesized at high pressures as starting materials and then laser heated on the beamline. The porosity, bubble number density, size distributions of bubbles and pore throats, as well as the tortuosity and connectivity of bubbles in the foams, were measured in three dimensions based on tomographic reconstructions of sample volumes. The reconstructed volumes were also used in lattice-Boltzmann simulations to determine viscous permeabilities of the samples. Connectivity of bubbles by pore throats varied from ~100 to 105 mm-3, and for each sample correlated positively with porosity and permeability. Although permeability increased with porosity, the relationship is complex; consideration of the results of this and previous studies of the viscous permeabilities of aphyric and crystal-poor magmatic samples demonstrated that at similar porosities the permeability could vary by many orders of magnitude, even in similar composition samples. More than 90 % of these permeabilities are bounded by two empirical power laws, neither of which identifies a percolation threshold. Comparison of the permeability relationships from this study with previous models (Degruyter et al. 2010; Burgisser et al. 2017) relating porosity, characteristic porethroat diameters and tortuosity demonstrated good agreement. However, modifying the Burgisser et al. (2017) model by using the maximum measured pore-throat diameter, instead of the average diameter, as the characteristic diameter produced a model that reproduced the lattice-Boltzmann permeabilities to within 1 order of magnitude. Measured correlations between the average bubble diameter and the maximum pore-throat diameter as well as between porosity and tortuosity in our experiments produced relationships that allow application of the modified Burgisser et al. model to predict permeability based only upon the average bubble diameter and porosity. The experimental results are consistent with previous studies suggesting that increasing bubble growth rates result in decreasing permeability of equivalent porosity foams. The effect of growth rate on permeability is hypothesized to substantially contribute to the multiple orders-of-magnitude variations in the permeabilities of natural magmatic samples at similar porosities.