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In this paper, we report on bi-dimensional Particle-In-Cell simulations performed in order to reproduce the laser-driven proton acceleration obtained when a commercial 200 TW Ti:Sa Laser hits a solid target. The laser-to prepulse contrast was enhanced using plasma mirrors yielding to a main-to-prepulse contrast of ~1012. We varied the pulse duration from 30 fs to 500 fs and the target thickness from 30 nm to several tens of μm. The on-target laser energy was up to 1.8J leading to an intensity in excess of 1020W cm-2. A comparison between numerical and existing experimental data [S. Fourmaux et al., Phys. Plasmas 20, 013110 (2013)] is performed, showing a good agreement between experimental results and simulations which confirms that for ultra-thin targets there is an optimum expansion regime. This regime depends on the target thickness and on the laser intensity: if the target is too expanded, the laser travels through the target without being able to deposit its energy within the target. If the target is not sufficiently expanded, the laser energy is reflected by the target. It is important to note that maximum proton energies are reached at longer pulse durations (in the 100 fs regime) than what is currently the best compression pulse length for this type of lasers (typically 20-30 fs). This duration, around 50-100 fs, can be considered a minimum energy transfer time between hot electrons to ions during the considered acceleration process. [ABSTRACT FROM AUTHOR]