Methods of Permeability Calculation for Vesicular Materials

Knowing the permeability of magma is key to understanding the degassing processes of volcanoes. Permeability is controlled by several factors including porosity, specific surface area, bubble connectivity, and pathway tortuosity, which makes calculation often difficult. However, because of the scale-dependence of permeabilities, measurements of permeability only provide correct values when measurements are taken at the appropriate scale of interest, which is not possible in the case of volcanic conduits. Preserved pumice samples give us smaller-scale snapshots of the bubble pathways in the volcano conduit at the time of eruption, which may be upscaled to a representation of the entire conduit. The permeability of this representation may then be calculated using various methods, each explored further here. The simplest of the methods is a Kozeny-Carman approach. In this case, a two-point correlation function is used to determine porosity and specific surface area, which can then be used in an equation to approximate permeability. The weakness of this method is that in vesicular materials, the small aperture radius between bubble connections is not accounted for. A second method, which does account for a smaller aperture radii, is the tube network model described by Jon Blower (Blower, 2001). This method treats gas flow through bubble networks similar to current in electrical circuits, where each aperture provides a certain resistance to flow. For this method, information is needed regarding each aperture in the bubble network. The Lattice-Boltzmann method provides a third way to calculate permeability. It is the most accurate of these methods, however, it typically is computationally expensive. In this presentation, we compare results of permeability determinations from measurements and the three theoretical/numerical approaches discussed above. We then discuss implications of permeabilities determined using these methods with respect to magmatic volatile degassing and related volcanic eruption dynamics.