Open-System Magmatic Processes: Energy-Constrained Recharge, Assimilation and Fractional Crystallization (EC-RAFC)

Geochemical data for igneous rocks provide conclusive evidence for the occurrence of open-system processes within magma bodies, the most critical of which are magma recharge (including enclave formation), assimilation of anatectic melt, and formation of cumulates by fractional crystallization. We have previously derived a model that tracks the composition of a magma body undergoing AFC; explicit in this model is accounting of country rock heating and the compositional effects of partial melting. The EC-AFC algorithm is based on solution of a system of differential equations that express conservation of energy (enthalpy), mass and species (trace elements and isotope ratios) (Spera and Bohrson 2001, Bohrson and Spera 2001). Here EC-AFC is extended to incorporate the effects of enthalpy, matter and species transport during magma recharge; this model, EC-RAFC, tracks the trace element and isotopic composition of melt, enclaves and cumulates as thermal equilibration is approached. 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. Solution of the EC-RAFC equations provides values for the average temperature of wallrock, mass of melt within the magma body, mass of cumulates and enclaves, mass of wall rock, mass of anatectic melt assimilated, concentration of t trace elements and i+s isotopic ratios in standing melt, cumulates, enclaves and anatectic melt as a function of the local temperature of standing magma. Input parameters include equilibration temperature, initial temperature and composition of magma, recharge magma, and wallrock, distribution coefficients, heat of fusion of wallrock and heats of crystallization of pristine and recharge magma, and isobaric specific heat capacities of all constituents. The magma recharge mass function is specified a priori and defines how recharge magma is added to standing magma (e.g., episodically, continuously). The present EC-RAFC simulator incorporates a weak coupling to major element mass balance and phase relations by means of a set of melt productivity functions based on laboratory experiments or Gibbs Energy minimization simulations (e.g., MELTS, Ghiorso 1997). Melt productivity functions prescribe the relationship between melt mass fraction and temperature. The EC-RAFC model, although a simplification of complex natural systems, is the first to examine systems characterized by magma recharge in a manner that self-consistently conserves energy, mass, and species. EC-RAFC not only provides an essential link between the physical and chemical controls governing complex open-system magma chambers, but also predicts complex geochemical behaviors that have analogues in natural magmatic systems; a number of these are examined in a companion abstract (Bohrson and Spera, this issue).