Mathematical Modeling of Nutrient Release from Capsulated Fertilizers

Abstract

The article is devoted to the study of reducing the technogenic load from high-dose nitrogen pollution of the soil layer by encapsulating granules of nitrogen fertilizers in slowly soluble phosphate-containing membranes. The process of dissolving and washing out of the primordial soil layer of the nutrients from urea, encapsulated by superphosphate shells in soil columns, was studied according to agrochemical techniques. The purpose of the work is to determine the parameters of the investigated process, based on which the previously developed physical model of soil washing of moving nitrogen forms, based on experimental data. The process of changing the loss of nitrogen from the soil when using different types of fertilizers depending on the amount of washing was studied by simulation. Mathematically, the process is described in general terms as a linear differential equation of the first order in partial derivatives. The solution of the equation under the initial and boundary conditions allowed to calculate the parameters of the model describing the nature of changes in the losses of nitrogen from the soil column. Comparison of calculated and experimental data showed a coincidence of values with a correlation coefficient above 0.96 for investigated nitrogen fertilizers with different composition of the phosphate-containing coating.

Improvement of Mathematical Model for Sedimentation Process

“…Figure 1 also presents the numerically obtained results of solving the particle sedimentation Equation (37). Approximation lines for all the data completely coincide with the analytically obtained function Equation (32).…”

“…Notably, the proposed approach can be applied not only for particle sedimentation and deposition problems but also for solving nutrient release problems from mineral fertilizers and the pneumatic classification of fine particles. Particularly, Equation (11) and its general solution Equation ( 27) allow us to clarify the concentration distribution for nutrients during their washing out from the fertilized soil [37]. The migration process of mineral components in the soil [38] can also be studied more precisely using the proposed fractional-calculus approach.…”

Effect of Superimposed Vibrations on Droplet Oscillation Modes in Prilling Process

“…Investigations of the liquid phase dispersion process in perforated shells [11] to create equipment for producing of nitrogen fertilizers [12] from their melts are considered in work on dust emission [13]. The dispersion performance during the mass transfer processes in pulsed solvent columns was presented in an article on dispersion performance [14].…”

Encapsulated organic–mineral fertilizers with nanoporous structure

“…To determine the effectiveness of the developed compositions of the encapsulated fertilizer shell, studies in soil columns were carried out to assess nitrogen leaching. Five washes were performed according to the standard procedure (Vakal et al 2020b). During the first wash, the amount of nitrogen washed from the shell with the biochar and calcium humate as a plasticizer was 2.3 times less than standard urea and 1.5 times less than the phosphate-containing shell, with the potassium humate as a plasticizer.…”