Upscaling permeability in anisotropic volcanic systems

Permeability is an important input to models of shallow magma ascent. It is a property that can exhibit anisotropy in volcanic magmas, rocks and edifices. Here we show that some important features of permeability anisotropy can be captured by a simple approach. The permeability of a layered medium can be described by a function that takes into account the angle between the direction in which pressure gradient acts, and the layering orientation. In the end-member case of flow parallel or perpendicular to the layering, the permeability of the whole system reduces to the arithmetic or harmonic means of the permeabilities of the constituent units, respectively. This implies that laboratory-scale measurements on homogeneous constituent layers can be upscaled to an effective permeability of a larger, multi-layered unit or edifice, including fractured systems. We outline the theoretical underpinning to these formulations, and provide experimental permeability data measured on anisotropic volcanic materials in order to validate this result. We show that this result implies that permeability parallel to layering or bedding must always be higher than that measured perpendicular to layering. Moreover, we emphasise that the choice of averaging method used to upscale permeability data on individual rock samples has important consequences for the validity of the derived values. We anticipate that these points will help move towards more realistic models of pressure evolution behaviour in volcanoes, and increase the utility of laboratory-derived data for volcano-scale modelling. (C) 2018 Elsevier B.V. All rights reserved.