ADModel-P is a detailed advection-dispersion mathematical model for the transport of nutrient species along rivers. The model has been calibrated and verified for a stretch of 54km of River Swale, UK, located between Catterick (National Grid Reference, NGR, SE225994508) and Crakehill (NGR SE426734). ADModel-P presented here is capable to simulate 2 species of phosphorus at high spatio-temporal resolution. The model accounts on field data (water flow and concentrations) and a detailed representation of phenomena which empowers good prediction efficiency of concentrations. ADModel-P also enables a detailed perspective on the modelling of pollutant transformations in the river stretch. Five classes of transformations are presented for the soluble reactive phosphorus (SRP) and organic phosphorus (OP). ADModel-P enabled generate empirical relations to express the dynamics of the following process rates: mineralization, sedimentation, resuspension, uptake and adsorption /desorption. These relations cater for a wide range of conditions with respect to water flow, temperatures and seasonality, for which the calibration and verification has been done.