To better understand the dynamical processes of partial melting, melt transport, and melt-rock reaction in the mantle, mass conservation equations for a two-porosity double lithology continuum have been developed using the method of volume averaging. Here the region of interest is treated as two overlapping continua occupied by a low-porosity peridotite matrix and a high-porosity dunite channel network. Conservation equations for the matrix and channel continua are coupled through mass transfer terms that include matrix dissolution and diffusive and advective mixing between the melt in the channel and that in the matrix. Essential features of the two-porosity double lithology model have been investigated through simple case studies. In general, the composition of the channel melt is a weighted average of the matrix melt extracted along the melting column (as a result of melt suction) and the matrix materials dissolved into the channel melt (as a result of matrix-channel transformation). Dissolution of pyroxene in the peridotite matrix into the channel melt and precipitation of olivine lowers the compatible trace element abundances in the channel melt. In the absence of matrix dissolution, the channel melt is equivalent to the aggregated or pooled matrix melt. The incompatible trace element abundance in the channel melt is dominated by the less depleted small-degree melts from the lower part of the melting column and not very sensitive to the details of how the melt suction rate and matrix-channel transformation rate vary spatially. The incompatible trace element abundances in the matrix melt and solid are very sensitive to the direction of melt flow across the matrix-channel interface, the magnitude and variation of the relative melt suction rate, and the depth of dunite channel initiation, and depend moderately on variations in channel volume fraction in the double lithology region. Percolation of the enriched channel melt into the more depleted residual matrix in the upper part of the melting column may provide a viable mechanism for late-stage melt refertilization or mantle metasomatism. Understanding the first-order characteristics of the channel and matrix melts and solids is essential in deciphering the melting and melt migration histories of residual mantle rocks and erupted basalts.
