Dynamic disequilibrium melting model with porous flow and diffusion-controlled chemical equilibration

Abstract

Melting of mantle peridotites is regarded as a dynamic process involving a differential flow between melt and solid. In this dynamic situation, chemical disequilibrium needs to be considered, because the time for chemical reaction between the melt and solid phases is limited. Here I present a new disequilibrium melting model which takes melt segregation associated with porous flow and diffusion-controlled chemical equilibration into account. The model is able to predict trace element fractionation during melting and melt segregation assuming chemical equilibrium only at the interface between melt and solid grains. The governing equations show that in a one-dimensional flow the chemical evolution of melt and solid is controlled by four dimensionless parameters, the partition coefficient, the total degree of melting, the efficiency of melt segregation, and the characteristic time for chemical equilibration. One of the important features of this system is that compositions of the melt and solid are mainly dependent on the characteristic time for chemical equilibration, and are almost independent of the efficiency of melt segregation. If local chemical equilibrium is achieved, trace element variations in the melt and solid are identical to those predicted by the batch melting model. The fractional melting model does not correctly predict the chemical variations even if the efficiency of melt segregation approaches infinity. When chemical disequilibrium is significant, neither the batch nor the fractional melting model can describe the chemical variations of the flow. For example, highly incompatible elements in the residual solid are enriched by several orders of magnitude more than when local equilibrium is achieved, whereas the melt is more depleted. These results suggest that disequilibrium processes may largely control chemical variations in igneous rocks, which can be assessed by the incompatible element variations, especially in the residual solid.