Numerical simulations are used to investigate parabolic pulse generation in tapered silicon optical fibers. The simulations are based on a realistic silicon fiber taper with micrometer-sized core dimensions, designed to have a decreasing normal dispersion profile, and include the effects of linear and nonlinear absorption. Evolution to the parabolic regime is quantified by a misfit parameter, and the optimum values for the input pulse and taper length are established. The results identify a distortion-free nonlinear propagation window for the transmission of optical pulses in normal dispersion silicon waveguides.