Diffusion chronometry (DC) is one of the novel petrological tools that allows us to determine the duration of residence of magma in different magmatic environments and corresponding timescales. The application of the phase-field modeling to the DC allows us allows us to carry out a quantitative investigation the influence of the various parameters on the texture evolution aiming at reconstructing the history of non-equilibrium grain structures. In this work, we have developed the solidification model which can be applied for three and more thermodynamic phases (e.g. Olivine-Plagioclase-Melt) in multicomponent magmatic systems and for unlimited quantity of crystals with different orientation and anisotropy. The phase-field modeling with anisotropic surface energies allows us to predict in detail the development of the texture and diffusion profiles in evolving crystals. The model of solidification in magmatic systems is based on the multicomponent models of metallic alloys, however, the thermodynamic data and anisotropy in minerals are different and need special techniques. For adaptation to mineralogical systems, we treat a real magmatic system and use thermodynamic data from the MELTS database to calculate the partitioning of elements between crystals and melts in a thermodynamically  consistent manner. The problems of the multicomponent phase-field modeling which appears during benchmark tests will be discussed.