A class of heterogeneous flow reactor model with internal storage is studied. Firstly, the global existence of the classical solution of the system is given. In order to overcome the difficulty caused by the singularity of the ratio term in the model, a class of nonlinear eigenvalue problems is introduced to establish the threshold dynamics of single species model in terms of the diffusion coefficient. Finally, the uniform persistence of the system is studied and the sufficient conditions for existence of the coexistence solutions are given.