Open-system magma chamber evolution: an energy-constrained geochemical model incorporating the effects of concurrent eruption, recharge, variable assimilation, and fractional crystallization

Significant petrogenetic processes governing the geochemical evolution of magma bodies include magma Recharge (including formation of ‘quenched inclusions ’ or enclaves), heating and concomitant partial melting of country rock with possible ‘contamination ’ of the evolving magma body (Assimilation), and formation and separation of cumulates by F ractional Crystallization (RAFC). Although the importance of modeling such open-system magma chambers subject to energy conservation has been demonstrated, the effects of concurrent removal of magma by eruption and/or variable assimilation (involv-ing imperfect extraction of anatectic melt from wall rock) have not been considered. In this study, we extend the EC-RAFC model to include the effects of Eruption and variable amounts of assimilation, Ax. This model, called EC-E 0RAcFC, tracks the compositions (trace elements and isotopes), temperatures, and masses of magma body liquid (melt), eruptive magma, cumulates and enclaves within a composite magmatic system undergoing simultaneous eruption, recharge, assimilation and fractional crystallization. The model is formulated as a set of 4 þ t þ i þ s coupled nonlinear differential equations, where the number of trace elements, radiogenic and stable isotope ratios modeled are t, i and s, respectively. Solution of the EC-E 0RAcFC equations provides values for the average temperature of wall rock (Ta), mass of melt within the magma body (Mm), masses of cumulates (Mct), enclaves (Men) and wall rock (M o a) and the masses of anatectic melt generated (Ma) and assimilated (cM a). In addition, t trace element concentrations and i þ s isotopic ratios in melt and eruptive magma (Cm, em, dm), cumulates (Cct, em, dm), enclaves (Cen, eor, d o r) and anatectic melt (Ca, eoa,