A mathematical model of a rotary kiln oxy-pyrolyser of sewage sludge is presented. The specific feature of the model is the consideration of the effect of axial staging of oxygen feeding to the reactor as one important key to the quality and productivity of the syngas, with a focus on the fate of tar and generation of soot. The gaseous oxidiser is fed to the reactor at multiple locations along its axis in a way that reproduces the paradigm of the Zwietering reactor. The fate of gaseous components and tar is followed using a simplified lumped-kinetic mechanism that was purposely developed. The model implements submodels for heat transfer among the phases and with the wall which embody radiative, convective and conductive terms. Homogeneous reactions in gas phase are modelled with a kinetic submodel that considers the generation of primary tars from devolatilisation of fuel and subsequent formation of secondary tars and soot by thermal cracking. The model validity has been confirmed by critical comparison with experimental literature data referring to a similar case. The steady operation of the oxy-pyrolyser is analysed in terms of fluxes of solid fuel and gaseous species, extent of fuel devolatilisation, temperature profiles of solid and gas phases along the reactor. The performance of the reactor is characterised in terms of process rate and chemical composition of the produced syngas, along with its heating value and thermal power. The influence of the distributed feeding is assessed by comparison with a benchmark case consisting of conventional non-distributed feeding.