Energy-constrained open-system magmatic processes I: General model and energy-constrained assimilation and fractional crystallization (EC-AFC) formulation

Geochemical data for igneous rocks provide definitive evidence for the occurrence of open-system processes in magma bodies, including Replenishment by intrusion of primitive magma, Assimilation of anatectic wallrock melt and cumulate formation by Fractional Crystallization. A general class of models (Energy Conserved-RAFC or EC-RAFC) can be constructed, which allow simulation of geochemical paths for trace elements and isotopic ratios for magma undergoing simultaneous replenishment, assimilation, and fractional crystallization during the approach to thermal equilibration. The general problem of EC-RAFC is formulated as a set of 3 + t + i + s coupled nonlinear ordinary differential equations, where the number of trace elements, radiogenic and stable isotope ratios simultaneously modeled are t, i and s, respectively. partial melting of wallrock, modeled as fractional melting, is incorporated, as are sensible and latent heat effects. Temperature-dependent partition coefficients are used to describe trace element distributions. Solution of the set of differential equations, with magma temperature (T(m)) as the independent variable, provides values for the average temperature of wallrock (T(a)), fraction of melt within the magma body (M(m)), mass of cumulates (M(r)) formed, mass of wallrock involved in the thermal interaction (M(q)(o)), mass of anatectic melt assimilated (M(a)*), the concentration of t trace elements (C(m)) and i + s isotopic ratios (epsilon (m)) in magma (melt plus cumulates) and in anatectic melt delivered to the evolving magma body. Input parameters include a user-defined equilibration temperature (T(eq)), the initial temperatures and compositions of magma, recharge magma, and wallrock, distribution coefficients and their temperature dependences, heats of fusion and crystallization, and isobaric specific heat capacities of the various constituents. For a priori defined magma recharge mass and T(eq), the mass of wallrock heated to T(eq) is computed and the geochemical trajectory of melt is determined as magma temperature approaches T(eq) from its starting value, T(m)(o). The effects of imperfect extraction of anatectic wallrock melt may be accounted for by introduction of an extraction efficiency factor. mathematical details of a simpler model. EC-AFC (no replenishment) are provided. Energy-constrained models have the advantage of linking thermal and chemical properties of magma chambers. Compared with 'classical' models that conserve mass and species only, they represent more complete assessments of the complex physicochemical dynamics governing the geochemical evolution of open-system magma bodies. Results of EC-AFC simulations demonstrate that geochemical trends can differ significantly from predictions based on 'classical' AFC even when recharge plays no role. Incorporation of energy conservation and partial melting into geochemical models allows important coupled effects to play their natural role.