LoRaWAN is the new transmission protocol for Low-Power Wide Areas (LPWA) networks. In addition to long range communications, one of the most solid arguments in favour of the LoRaWantechnology is its ability to operate at orthogonal spreading factors (SFs). This enables simultaneous transmissions at different data rates on the same frequency channel. But Recently, it has been shown that transmissions at different SFs are not perfectly orthogonal which generates cross-SF interferences (i.e. interferences between different spreading factors' transmissions). Therefore, we propose here an analytical model of a single cell LoRaWAN under unsaturated traffic, duty cycle and multi-channel deployment conditions. The model considers both perfect and imperfect SF orthogonality scenarios. The network performance are then derived in terms of achievable throughput at the gateway as a function of the offered load, the number of received packets per device and the percentage of successful transmissions. All the Results show that if spreading factors are assumed to be orthogonal, the capture effect improves the network performance in comparison with the theoretical pure Aloha access scheme. Whereas, the consideration of imperfect SF orthogonality revises the LoRaWAN performance downward.