The BEaTriX (Beam Expander Testing X-ray) facility, being assembled at INAF-Brera Astronomical Observatory, will represent an important step in the acceptance roadmap of Silicon Pore Optics (SPO) mirror modules, and so ensure the final angular resolution of the ATHENA X-ray telescope. A paraboloidal mirror, manufactured at INAF-Brera, will provide a collimated X-ray beam to a monochromating system and to a beam expansion unit, enabling the full illumination of the mirror modules under test with a broad, highly monochromatic, and parallel X-ray beam. Such a beam will be used to directly diagnose SPO modules in their focusing performances. This requires, indeed, the expanded beam to have a divergence smaller than the expected angular resolution of the modules under test. This condition is subject, in turn, to the optical quality and to the alignment of the optical components. Aiming at establishing the final angular resolution that can be reached and the respective fabrication/positioning tolerances, we have been dealing with a comprehensive set of optical simulations. Modeling based on wave optics and ray-tracing was carried out to predict the collimation performances of the paraboloidal mirror, including the effect of surface errors obtained from metrology. Ray-tracing routines were subsequently employed to simulate the full beamline. This paper reports the simulation results and the methodologies we have adopted.