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 occu rrence 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 simulat ion of geochemical paths for trace elements and isotopic ratios for magma u ndergoing simultaneous replenishment, assimilation, and fractional crystall ization during the approach to thermal equilibration. The general problem o f EC-RAFC is formulated as a set of 3 + t + i + s coupled nonlinear ordinar y differential equations, where the number of trace elements, radiogenic an d stable isotope ratios simultaneously modeled are t, i and s, respectively . partial melting of wallrock, modeled as fractional melting, is incorporat ed, as are sensible and latent heat effects. Temperature-dependent partitio n coefficients are used to describe trace element distributions. Solution o f the set of differential equations, with magma temperature (T-m) as the in dependent 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)), m ass of anatectic melt assimilated (M-a*), the concentration of t trace elem ents (C-m) and i + s isotopic ratios (epsilon (m)) in magma (melt plus cumu lates) and in anatectic melt delivered to the evolving magma body. Input pa rameters include a user-defined equilibration temperature (T-eq), the initi al temperatures and compositions of magma, recharge magma, and wallrock, di stribution coefficients and their temperature dependences, heats of fusion and crystallization, and isobaric specific heat capacities of the various c onstituents. 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 ma y be accounted for by introduction of an extraction efficiency factor. math ematical details of a simpler model. EC-AFC (no replenishment) are provided . Energy-constrained models have the advantage of linking thermal and chemi cal properties of magma chambers. Compared with 'classical' models that con serve mass and species only, they represent more complete assessments of th e complex physicochemical dynamics governing the geochemical evolution of o pen-system magma bodies. Results of EC-AFC simulations demonstrate that geo chemical trends can differ significantly from predictions based on 'classic al' AFC even when recharge plays no role. Incorporation of energy conservat ion and partial melting into geochemical models allows important coupled ef fects to play their natural role.