The Photo Injector Test facility at DESY, Zeuthen site (PITZ), offers the unique possibility to study and demonstrate the self-modulation of long electron bunches in plasma. A set of numerical simulations with the particle-in-cell code OSIRIS has been carried out for a better understanding of the process. Of particular interest is the measurement of the energy modulation induced to the beam itself by means of the generated wakefields in plasma. It will reflect the key properties of the accelerating electric fields such as their magnitude and their phase velocity, both of significant importance in the design of experiments relying on this technique.