Mathematical model for N release from polymer-coated controlled-release fertilizers

Controlled release of nutrients from coated fertilizer granules is desired for optimal uptake by plants and crops. We studied the release of amide nitrogen, a non-electrolyte, from a polymer-coated spherical fertilizer granule, having varying influence factors. The release course was divided into three stages: the lag period, the linear stage and the decay stage. An exact mathematical model based on Fick's Second Diffusion Law was developed to predict the release rate of a polymer-coated controlled-release fertilizer using equations of mathematical physics and numerical analysis methods, and Laplace transform and Residue theory were used to solve the equations. From the explicit mathematical model, an approximate solution for the nitrogen release was obtained. The model showed that nitrogen release was mainly controlled by the types of coating materials and their membrane thickness. The models can be used to describe the release rate under different operating conditions. Detailed and approximate solutions were developed and compared with the nutrient release experiments, and different fertilizers were used to verify the approximate release model. Four polymer-coated controlled-release fertilizers, the thermoplastic resin coated fertilizer (1#, l=0.0586 cm; 3#, l=0.0065 cm), and alkyd resin coated fertilizer (2#, l=0.0463 cm; 4#, l=0.0058 cm), were used in nitrogen release experiments. Release experiments were conducted using the methods of water extraction from GB/T 23348-2009, at 25℃. The effective diffusion coefficient of amide nitrogen was fixed. The experiments showed the nitrogen was mainly released in the linear stage. The release period of alkyd resin coated fertilizers was shorter than the thermoplastic resin coated fertilizers under almost the same membrane thickness. The cumulative percentage of nitrogen release decreased when the membrane thickness increased. The cumulative release profile of nitrogen from the thermoplastic resin coated fertilizer and alkyd resin coated fertilizer into water agreed with the prediction of the model on the whole. The calculated and experimental values of nitrogen release of the thermoplastic resin coated fertilizer in the Lag and Decay stage was better fit than the linear, the relative error range was: 0-37.55%. The best fit between the calculated and experimental values of nitrogen release of the alkyd resin coated fertilizer in the linear stage, the relative error range was: 0-23.06%, and the relative error increased when the release time increased. Understanding these effects quantitatively is very useful in determining the types of coating materials and coating width to use while manufacturing such granules.