Mass balance calculations

Ayers et al. (2022) The solubility of titanite in silicate melt determined from growth and dissolution experiments. Contributions to Mineralogy and Petrology.
Mass
balance calculations were performed for seven growth experiments that had only
titanite and glass as run product phases. Weighted nonlinear least squares
regression was used with the constraints that the weight fractions for titanite
and glass were <= 1 and >= 0.01 and that the sum of weight fractions
equal one. FeO was excluded due to iron loss during the experiments, and MnO
and P2O5 were excluded because their concentrations were
near the detection limit so that relative errors on their concentrations were
high. Calculated weight fractions of titanite ranged from 0.01 to 0.07. Oxides
included in the mass balance calculations and their average absolute values of
relative errors were SiO2 4%, Al2O3 6%, Na2O
9%, K2O 11%, CaO 15%, MgO 41% and TiO2 15%. MgO relative
errors were higher because in some experiments the starting material had very
low MgO concentrations.