A dynamic model of polymer wet spinning coagulation process is proposed in this article. The model is based on the double diffusion phenomenon, phase separation process, continuity balance, and momentum balance of the entire coagulation process. The uniqueness of the model lies in its dynamic feature. The model can simulate the system's dynamic response to variations in system inputs/parameters. Steady-state system solutions can also be produced as the long-time solutions of the dynamic model; a settling time can be observed at the same time. This paper employs a computationally efficient method of lines numerical algorithm for solving the dynamic model. A simulation experiment on a selected non-solvent-solvent-polymer ternary system is carried out to verify the model as well as the numerical method. The dynamic simulation results are analyzed and discussed. At the end of the article, h-refinement and p-refinement are used to confirm the spatial convergence of the numerical solutions. (C) 2016 American Institute of Chemical Engineers