Formation damage due to chemical reactions or physical failure of rock is a well-known issue in the oil and gas industry. In this paper, we look at the changes of injectivity at water injectors located in unconsolidated formations as a result of sand channelization. In these situations, sand particles migrate from the formation matrix toward the wellbore and consequently affect permeability of the formation and completion components like frac-packs or gravel-packs. To model this phenomenon, we propose a model that decomposes the sand matrix into two different phases by means of their volumetric fractions. The first phase consists of the immobile granular phase while the other is the fraction of grains that are detached from the matrix and carried away by the fluid. The ratio of these two phases evolves over time by means of erosion and deposition. A finite element code is developed for numerical implementation of this model for different reservoir properties. The results show how the porosity evolves over time around the wellbore by the formation of channels that enhance the flow, however, upon well shut-in, Flowback induced by the water hammer effect brings a large amount sand into the well and fill it up. A study of the effect of frac-packs which are typical completions for wells targeting soft formations is performed to demonstrate potential damage of repetitive shut-ins on injectivity in these wells. The presented model appears as a robust tool to predict sand production in different completion systems to achieve more sustainable injection treatments.