Modeling of nitrogen release in urea-modified lignin matrix

Urea, as the most widely used fertilizer, has the highest nitrogen loss in aqueous media. Urea-modified lignin matrix as a biodegradable and inexpensive bio-polymer can become a controlled-release fertilizer with commercial capability; Therefore, release models investigate is very important. Two-dimensional partial differential equation was solved analytically considering time and radius as two independent variables in spherical coordinates for infinite volume and compared to the results for finite volume of liquid. In order to validate the model’s results, equal amounts of melted urea and lignin acetylated were mixed for preparation of matrix using spherical frame. The amount of nitrogen release from the matrix of lignin in water was measured by Kjeldahl method at different time intervals. Presented models were able to predict release of urea for the infinite and finite fluid volume with R2 equivalent to 9967/0 and 9946/0, respectively. Moreover, empirical models were applied to predict the release pattern including: Power, Modified Schwartz and Suggested Modified hyperbolic model. Among the models used in this research, obtained analytical model for infinite volumes, finite and modified hyperbolic model had the highest accuracy, respectively.