Computation of phase equilibria by linear programming: A tool for geodynamic modeling and its application to subduction zone decarbonation

An algorithm for the construction of phase diagram sections is formulated that is well suited for geodynamic problems in which it is necessary to assess the influence of phase transitions on rock properties or the evolution and migration of fluids. The basis of the algorithm is the representation of the continuous compositional variations of solution phases by series of discrete compositions. As a consequence of this approximation the classical non-linear free energy minimization problem is trivially solved by linear programming. Phase relations are then mapped as a function of the variables of interest using bisection to locate phase boundaries. Treatment of isentropic and isothermal phase relations involving felsic and mafic silicate melts by this method is illustrated. To demonstrate the tractability of more complex problems involving mass transfer, a model for infiltration driven-decarbonation in subduction zones is evaluated. As concluded from earlier closed system models, the open-system model indicates that carbonates are likely to persist in the subducted oceanic crust beyond sub-arc depths even if the upper section of the oceanic mantle is extensively hydrated. However, in contrast to more simplistic models of slab devolatilization, the open-system model suggests slab fluid production is heterogeneous and ephemeral. Computed seismic velocity profiles, together with thermodynamic constraints, imply that for typical geothermal conditions serpentinization of the subducted mantle is unlikely to extend to > 25 km depth and that the average water-content of the serpentinized mantle is < 2 wt.%.