FACTORS CONTROLLING PERMEABILITY-POROSITY RELATIONSHIPS IN MAGMA

Abstract

A model has been developed to investigate the sensitivity of magma permeability, k, to various parameters. Power-law relationships between k and porosity φ are revealed, in agreement with previous experimental and theoretical studies. These relationships take the form \(\) \(\hat k = k/r^2 = a(\phi - \phi _{cr} )^b \) where r is the mean bubble radius, φ cr is the percolation threshold below which permeability is zero, and a and b are constants. It is discovered that \(\) \(\hat k - \phi \) relationships are independent of bubble size. The percolation threshold was found to lie at around 30% porosity. Polydisperse bubble-size distributions (BSDs) give permeabilities around an order of magnitude greater than monodisperse distributions at the same porosity. If bubbles are elongated in a preferred direction then permeability in this direction is increased, but, perpendicular to this direction, permeability is unaffected. In crystal-free melts the greatest control on permeability is the ease of bubble coalescence. In viscous magmas, or when the cooling time-scale is short, bubble coalescence is impeded and permeability is much reduced. This last effect can cause variations in permeability of several orders of magnitude.