Dewatering processes are invariably encountered in the chemical manufacturing and processing of various bioproducts. In this study, Computational Fluid Mechanics (CFD) simulations and theory are utilized to model and optimize the dewatering of commercial nanofiber suspensions. The CFD simulations are based on the volume-averaged Navier-Stokes equations, while the analytical model is deduced from the empirical Darcy's law for dewatering flows. The results are successfully compared to experimental data on commercial cellulose suspensions obtained with a Dynamic Drainage Analyzer (DDA). Both the CFD simulations and the analytical model capture the dewatering flow profiles of the commercial suspensions in an experiment using a constant pressure profile. However, a temporally varying pressure profile offers a superior dewatering performance, as indicated by both the simulations and the analytical model. Finally, the analytical model also predicts an optimized number of pressure pulses, minimizing the time required to completely dewater the suspension.