Electrochemical charging of nanocrystal films opens up new possibilities for designing quantum dot-based device structures, but a solid theoretical framework of this process and its limitations is lacking. In this work, drift-diffusion simulations are employed to model the charging of nanocrystal films and gain insight into the electrochemical doping process. Through steady state simulations it is shown that the Fermi level and doping density in the nanocrystal film depend on the concentration of the electrolyte in addition to the value of the applied potential. Time-resolved simulations reveal that charging is often limited by transport of electrolyte ions. However, ion transport in the film is dominated by drift, rather than diffusion, and the concentration profile of ions differs substantially from concentration profiles of diffusing redox species at flat electrodes. Classical electrochemical theory cannot be used to model this type of mass transport limited behavior in films of nanocrystals, so a new model is developed. We show that the Randles-Ševčík equation, which is derived for electrochemical species diffusing in solution, but is often applied to films as well, results in a significant underestimation of the diffusion coefficients of the charge compensating electrolyte ions.