Mineral precipitation in an open fracture plays a crucial role in the evolution of fracture permeability in rocks, and the microstructural development and precipitation rates are closely linked to fluid composition, the kind of host rock as well as temperature and pressure. In this study, we develop a continuum thermodynamic model to understand polycrystalline growth of quartz aggregates from the rock surface. The adapted multiphase-field model takes into consideration both the absolute growth rate as a function of the driving force of the reaction (free energy differences between solid and liquid phases), and the equilibrium crystal shape (Wulff shape). In addition, we realize the anisotropic shape of the quartz crystal by introducing relative growth rates of the facets. The missing parameters of the model, including surface energy and relative growth rates, are determined by detailed analysis of the crystal shapes and crystallographic orientation of polycrystalline quartz aggregates in veins synthesized in previous hydrothermal experiments. The growth simulations were carried out for a single crystal and for grain aggregates from ... mehra rock surface. The single crystal simulation reveals the importance of crystal facetting on the growth rate; for example, growth velocity in the c-axis direction drops by a factor of ~9 when the faceting is complete. The textures produced by the polycrystal simulations are similar to those observed in the hydrothermal experiments, including the number of surviving grains and crystallographic preferred orientations as a function of the distance from the rock wall. Our model and the methods to define its parameters provide a basis for further investigation of fracture sealing under varying conditions.