Cellulose aerogels are the most well-studied biopolymer-based systems in the literature, yet we lack a complete understanding of the underlying gelation mechanism, as well as that of the effect of solvent exchange on the topology of their network. This work presents a coarse-grained model describing the gelation kinetics in cellulose aerogel systems. A discrete element model is employed to generate the cellulose structure, and the solvents are modeled implicitly. Langevin dynamics is applied to solve the system of Newtonian equations. The model successfully generates the structure of the cellulose gel, hydrogel, alcogel, as well as aerogel. A model parameter sensitivity analysis is presented, and the results of the model are validated against the experimental data. The model provides insights into the mechanism of gelation while also shedding light on the morphological alterations resulting from the washing, solvent exchange, and drying steps.