Effective shear and bulk viscosity of partially molten rock based on elastic moduli theory of a fluid filled poroelastic medium

SUMMARY The effective bulk and shear viscosity of the matrix of a partially molten rock are important properties for the process of melt migration and matrix compaction. A set of porosity-dependent effective bulk and shear viscosity models is presented based on a self-consistent poroelastic formulation for partially molten rock where the melt occurs in spherical, ellipsoidal, film-like or tubular inclusions. For these melt geometries a graphical user interface operated MATLAB program is provided which allows the calculation of effective bulk and shear viscosities as a function of porosity, as well as effective elastic moduli and seismic velocities. For all melt geometries an inverse porosity—dependence of the effective bulk viscosity is found. Depending on the assumed melt geometry, this formulation predicts both the effective bulk and shear viscosity to drop to zero at and above finite melt fractions of 20–50 per cent. Fitting equations are derived allowing direct implementation into two-phase flow melt–matrix formulations.