The Electron-Ion collider (EIC) will be the ultimate facility to study the dynamics played by the colored quarks and gluons to the emergence of the global phenomenology of the nucleons and nuclei as described by Quantum Chromodynamics. The physics programs will greatly rely on efficient particle identification (PID) in both the forward and the backward regions. The forward and the backward RICHes of the EIC have to be able to cover wide acceptance and momentum ranges; in the forward region a dual radiator RICH (dRICH) is foreseen and in the backward region a proximity-focusing RICH can be foreseen to be employed. The geometry and the performance studies of the dRICH have been performed as prescribed in the EIC Yellow Report using the ATHENA software framework. This part of our work reports the effort following the call for EIC detector proposal the studies related to the forward and the backward RICHes performance. In the forward region, dRICH performance showed a pion-kaon separation from around 1 GeV/c to 50 GeV/c at a three sigma level; the proximity focusing RICH (pfRICH) foreseen for the backward region can reach three sigma separation up to 3 GeV/c for e/\(\pi\) and up to 10 GeV/c for \(\pi\)/K mass hypothesis.