We present a numerical model that simulates the evolution of precipitates and the diffusion of interstitial oxygen in Czochralski silicon. The growth and/or dissolution of each precipitate and the local concentration of interstitial oxygen with which the precipitates interact are followed as a function of time. We treat realistic densities of discrete, interacting precipitates and determine how the precipitate density influences the extent of the precipitation. The model also treats oxygen outdiffusion and the formation of precipitate-free or denuded zones. We apply the model to previous experimental data on the time dependence of precipitate growth and to the development of denuded zones during intrinsic gettering.