Most of the attractive electrical properties of carbon nanotubes (CNT), such as 1D transport and very large mobilities, are also shared by carbon nanoribbons (CNR), which can potentially overcome the growth control problems of CNTs . Since experimental demonstration of CNR field effect transistors (FET) is at an early stage, simulation studies are important to investigate their theoretical limits. In the literature one can find simplified semiclassical models  and full atomistic tight binding (TB) models . Both have limitations: in the former case, direct and band-to-band tunneling effects are ignored, in the latter deep physical insight is achieved at the price of very long computational times. Here we present a hierarchical approach to the modelling of CNR-FETs, which blends together first-principle density functional theory (DFT) for subband calculations, full 2D atomistic TB modelling, and effective mass (EM) 1D quantum transport modelling, improved with nonparabolic (NP) corrections. The approach is applicable to armchair semiconductor CNRs. Moving along the hierarchy of models from the most physically in-depth (DFT) to the most details-free (EM) approach, more accurate models are used to calibrate the parameters of less accurate ones. In-depth models are suitable for the simulation of very small FETs (both narrow and short ribbons), but are impractical for devices of large sizes, which however are the ones that can be fabricated with the state-of-the-art technology. For such devices, where quantum effects already play a major role, the NPEM approach is quite effective. We compare simulation results from the various approaches for FETs based on very narrow CNRs, namely (6,0) with W = 0.6 nm and (12,0) with W = 1.35 nm. We show that the NPEM model can fairly well describe the I-V characteristics in all bias conditions, including the regimes dominated by direct or band-to-band tunneling, provided first-order NP corrections are properly included. A (40,0) CNR-FET, corresponding to a more realistic W = 4.8 nm, is investigated by means of the NPEM approach, suggesting the possibility of an optimization study.