Application of the Richards function to nitrogen release from coated urea at a constant temperature and relationships among the calculated parameters

Abstract

The Richards function used as an asymmetric growth function was applied to describe the cumulative amount of nitrogen released from coated urea at a constant temperature. The description was very precise. The characteristics of the nitrogen release were expressed using four parameters of the Richards function, regardless of the fertilizer group. The first parameter (N), indicating the maximum amount released, approximated the nitrogen content of the fertilizer. The second parameter (d), which characterizes the shape of the release curve, enabled to distinguish slow-release from delayed-release fertilizers. Temperature did not effect appreciably these two parameters. The third parameter (k), indicating the release rate, followed the Arrhenius equation, in which the apparent activation energy (E_a ) was approximately constant for all the fertilizers. The fourth parameter (t_i ), which indicates the time to the inflection point, corresponding to the time to the point where the maximum amount of nitrogen releases per unit time, could be calculated from the other parameters (d, k). Accordingly, the amount of nitrogen released from coated urea at a constant temperature can be described using three parameters (N, d, k). The Richards function is therefore superior to the Bertalanffy function, which had been used until now, since it can describe the nitrogen release more exactly while using the same number of parameters.

Key Words:

• Arrhenius equation
• Bertalanffy function
• coated urea
• nitrogen release
• Richards function