A model for the release of sulfur from elemental S and superphosphate

Abstract

A mathematical model was developed to predict the release of sulfate from elemental S (S0) and gypsum in single superphosphate. The release algorithm is based on the observation that release is linearly related to particle surface area. Release rates under various conditions could then be described by the change in radius for each time increment, which allows easier comparison of release rates between different particle sizes. A model based on spherical particles was found to be adequate in accounting for the range of particle shapes found in crushed agricultural S0. Release rates calculated from experimental data range from 0.07 to 0.45µm/d depending on environmental conditions. Equations for incorporating the effects of environmental variables and the release of S from S0 and from the gypsum component of single superphosphate (SSP) were developed from the literature, and were incorporated within a larger model of S cycling. The model predicted that after 72 days, 99% of the S in SSP would have been released, compared to a release after one year of 54% of the S in sulfur-fortified superphosphate, and 23% of that in crushed agricultural grade S0. The model provides a means of assessing the effect of the particle size of S0 on release rates and should allow the formulation of fertilizers that supply S at a rate closer to the rate of plant uptake.