PERMEABILITY OF A PARTIALLY MOLTEN ROCK

Recent geophysical and geochemical studies have generated a lot of discussion on melt segregation/migration processes in the crust and mantle. To address these problems, a better understanding of permeability of partially molten rocks is essential. In the past two decades, significant progress has been made in advancing our knowledge of fluid phase distribution in partially molten rocks. For instance, the melt distribution in an isotropic two-phase system under equilibrium conditions is well defined. In such a system, all the melt channels are identical and they are either all interconnected or isolated depending upon the dihedral angle and the melt fraction of the system. Therefore, a simple analytical relationship can be derived between permeability (k), grain size (d) and melt fraction (f): k=d ²f ²/C [e.g., von Bargen and Waff, 1986]. However, any anisotropy, be it non-isostatic stress, anisotropic interfacial energy, or the third phase, will invalidate this relationship. In this study, we developed a network model to calculate permeability as a function of distributions of the dihedral angle and melt fraction. This 3-D network model is 84x84x57, which contains 5110 grains and 65804 channels. In our model, each channel is treated as a prism with a length of the grain boundary. The cross-sectional area of each prism is determined by a given dihedral angle and a melt fraction. Three dihedral angle distributions are used as input data: single value of 60°, a normal distribution between 20° to 100°, a uniform distribution between 20° and 100°. Our results show that the permeability of an anisotropic system can be significantly different from the calculated permeability of an isotropic system with the same median dihedral angle using the power law relationship described above.