Modeling controlled nutrient release from a population of polymer coated fertilizers: statistically based model for diffusion release.

A statistically based model for describing the release from a population of polymer coated controlled release fertilizer (CRF) granules by the diffusion mechanism was constructed. The model is based on a mathematical-mechanistic description of the release from a single granule of a coated CRF accounting for its complex and nonlinear nature. The large variation within populations of coated CRFs poses the need for a statistically based approach to integrate over the release from the individual granules within a given population for which the distribution and range of granule radii and coating thickness are known. The model was constructed and verified using experimentally determined parameters and release curves of polymer-coated CRFs. A sensitivity analysis indicated the importance of water permeability in controlling the lag period and that of solute permeability in governing the rate of linear release and the total duration of the release. Increasing the mean values of normally distributed granule radii or coating thickness, increases the lag period and the period of linear release. The variation of radii and coating thickness, within realistic ranges, affects the release only when the standard deviation is very large or when water permeability is reduced without affecting solute permeability. The model provides an effective tool for designing and improving agronomic and environmental effectiveness of polymer-coated CRFs.