  In this work, we model and simulate the performance of a quantum key
distribution (QKD) downlink from a low earth orbit (LEO) small satellite to an
optical ground station (OGS), as integral part of the concept and preliminary
design phase of the QuantSat-PT mission. By modelling and simulating in detail
downlink transmission channel effects, with emphasis on turbulent and
atmospheric losses for BB84 and E91 protocols, we find a consistent set of
values for the performance envelope that resolves ambiguities of mission
experimental data that had been reported previous to this work. We obtain for
the 4-state BB84 protocol a sifted key rate and Quantum Bit Error Rate (QBER)
of 32.1 kbit/s and $4\%$, respectively, for zenith at 750 km orbit. For the E91
protocol the Clauser, Horne, Shimony and Holt (CHSH) test was performed
resulting in a correlation factor of $S \in[-2.63\pm0.02,-1.91\pm0.03]$ for the
mission. The consistency of these results with the state of the art simulators
and its relevance on experimental satellite based QKD is discussed.
