Plugging of flow channels by cohesive particles is a critical problem in medicine, energy technology, petroleum, and communal water distribution. Plugging risk management would benefit from reliable numerical models of the process. However, only simplified models incapable of reproducing the entire process at industrially-relevant scales have been reported so far. Bridging the gap, in this paper, we present a pragmatic Eulerian-Eulerian model of plugging in pipes with local flow restrictions. The model accounts for the cohesion of particles via rheological expressions. The model consists of several user-defined modules incorporated in the commercial STAR-CCM+ and adaptable to other CFD packages. We further demonstrate how this model validates against flow loop experiments on plugging in ice-in-oil slurries.