Modeling NPK release from spherically coated fertilizer granules

Controlled release of nutrients from fertilizers is desired for its optimal uptake by plants and crops. In our previous study [22], we considered saturation of a non-electrolytic nutrient and its release from a spherically coated fertilizer granule, assuming only molecular diffusion. In the present study, release of three types of nutrients (NPK) from their commonly used commercial fertilizer sources, stuffed in a coated spherical fertilizer granule is investigated using both molecular and ionic diffusions. One of the nutrients is potassium chloride (KCl), a strong electrolyte, the other is diammonium phosphate ((NH4)2HPO4), a weak electrolyte, and the third is urea ((NH2)2CO), a non-electrolyte. The release takes place from the granule’s surface area in contact with the soil. The contact area is varied from almost a point to the lower hemisphere with the help of a parameter. The latter case helps to evaluate the release time for basal form of fertilizer application. The effects of granule radius, nutrients release rate, contact area, association constant, pH, and temperature on the release time of nutrients are studied. Variations in release time are much more pronounced from a spherical granule of larger radius having almost point contact with alkaline soil at higher temperatures and for a weak electrolyte of lower association constant. The release time is computed using the techniques of deterministic mathematical modeling and computer simulation. Sensitivity analysis has also been done by giving small variations in the parameters of pH modulator, in the ionic diffusion coefficients of strong- and weak-electrolytes and evaluating root mean squared deviations (RMSD) in release time. Values of RMSDs are negligible, establishing the stability and accuracy of the technique used. Such studies are useful in manufacturing coated spherical granules according to the varying soil conditions, educating the farmers about optimal use of the granules, and also deciding the basal or dispersal form of application of nutrients according to the crop.