A role for percolation theory in analysis of gas permeability of magma

Abstract

Permeability data for natural and experimental products of magma that have been reported by sev-eral studies are reanalyzed on the basis of percolation theory. I use a powerlaw relationship between gas permeability k and porosity with a critical porosity c and a critical exponent e in the form, k (c) e , after reviewing some dependences of c and e on characteristics of porous media. As a result, the k data of silicic magmas from nonexplosive eruptions are found in a whole region containing two models of continuum percolation: Swisscheese model (c 0%, e 4.5) and inverted Swisscheese model (c 30%, e 2), and no data clearly denotes c much higher than 30%. I also point out that it is necessary to consider careful textural characteristics of porous samples in analyzing the k data in order to assess the process of formation of the texture adequately. Important textural characteristics are i) crosssectional area of gas channel used for nor-malizing k because of estimating appropriate values of c and e, ii) elongation of pore and align-ment of the direction, and iii) sample scale defined as a ratio of the sample length to a characteristic length of the major axes of elongated pores, because c depends on the degree of the elongation, the alignment and the sample scale.