Construction of metamorphic reactions for high temperature zone of Borujerd granitoid metamorphic aureole based on algebraic model

Application of mathematics increasing in science in recent years, cause the mathematical models use to explain the geological processes. The researchers introduced a method based on mathematical calculations and algebraic model for metamorphic reactions. Pelitic metamorphic aureole is formed in North of Borujerd granitoid complex in the region east of Borujerd city. In this research for the first time, using a mathematical method for metamorphic reactions for high temperature of Pelitic metamorphic aureole based on algebraic model. Based on petrography, mineral assemblages of a rock are known and a thermodynamic system and components could be drive. SiO2, Al2O3, MgO, FeO, K2O and H2O Accepted as components and the system KFMASH chosen for calculation. Based on mineral assemblages, metamorphic reactions calculated using 6 by 6 and 6 by 8 matrices. Components put in Matrix and when Matrix’s elements below the diagonal are zero, then the calculation is applied over the second matrix to find metamorphic reactions. Equilibrium reactions could be written based on both microprobe analyses and general mineral formula. The main reactions in the intermediate zones toward the contact, in order from low to high temperature, are cordierite formed after reaction of biotite, quartz and andalusite followed by equation of andalusite to sillimanite. Potassium feldspar appears in the same rocks with sillimanite. Potassium feldspar and cordierite formed close to the contact zone, Petrographic result confirmed paragenetic minerals which appeared in algebraic analysis. The results show that reactions constrain based on algebraic analysis, could be used to estimated pressure and temperature in petrologic grids