Factors controlling permeability–porosity relationships in magma

A model has been developed to investigate the sensitivity of magma permeability, k, to various parameters. Power-law relationships between k and porosity J are revealed, in agreement with previous experimental and theoretical studies. These relationships take the form % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavTnhis1MBaeXatLxBI9gBae % rbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyavP1wzZbIt % LDhis9wBH5garqqtubsr4rNCHbGeaGqiVCI8FfYJH8sipiYdHaVhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfeaY-biLkVcLq-JHqpepeea0-as % 0Fb9pgeaYRXxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaabau % aaaOqaaiqbdUgaRzaajaGaeyypa0Jaem4AaSMaei4la8IaemOCai3a % aWbaaSqabeaacqaIYaGmaaGccqGH9aqpcqWGHbqycqGGOaakcqaHgp % GzcqGHsislcqaHgpGzdaWgaaWcbaGaem4yamMaemOCaihabeaakiab % cMcaPmaaCaaaleqabaGaemOyaigaaaaa!4CE4! ^(k)] = k/r² = a(f- f_cr )^b\hat k = k/r^2 = a(\phi - \phi _{cr} )^b where r is the mean bubble radius, J_cr is the percolation threshold below which permeability is zero, and a and b are constants. It is discovered that % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavTnhis1MBaeXatLxBI9gBae % rbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyavP1wzZbIt % LDhis9wBH5garqqtubsr4rNCHbGeaGqiVCI8FfYJH8sipiYdHaVhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfeaY-biLkVcLq-JHqpepeea0-as % 0Fb9pgeaYRXxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaabau % aaaOqaaiqbdUgaRzaajaGaeyOeI0IaeqOXdygaaa!3CDB! ^(k)] - f\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.