Waste valorization, value recovery is the process of waste products or residues from an economic process being valorized by reuse or recycling in order to create economically useful materials. The term comes from practices in sustainable waste management. This study mainly deals with the purpose of bio-fertilization and the transportation of nutrients to the soil. Biofertilizers play an essential role in colonizing the rhizosphere and supply of NPK for promoting growth to the host plants. Continuous application of chemical fertilizers exhibited detrimental effects on the environment and Agroecosystems. Therefore, the development of bio-organic fertilizers has been a solution to the problem. This study deals with the soil diffusion kinetics and N, P, and K constituent distribution for the bio-fertilizer and the calcium to the soil. The mathematical models have been applied to determine the liberation of nutrient sources for plant growth, transport of fertilizer components in the soil, and absorption in plant roots for better productivity. The three important sections have been investigated which take part actively in this whole process. Firstly, the liberation of nutrient components from fertilizer to soil and water. Secondly transportation of plant nutrients through the soil-water system by diffusion mechanism. And finally, absorption of plant nutrients in plant roots by soil diffusion kinetics. The dissolution rate of the applied fertilizer depends upon the temperature, surface area, pH and ionic groups bonded with the molecule. Therefore, the dissolution rate was considered on equilibrium concentration of nutrients in soil water mixture, and consequently, the governing equation can be written as . Using kinetic study, the rate constant and order of dissociation of fertilizer evaluated by plotting vs. .The concentration profile of the bio-organic fertilizer can be calculated by the equation: .For bio-organic fertilizer
The solution for the diffusion kinetics as represented in the above equation indicates the concentration of fertilizers in different positions with respect to time, and it may calculate on the surface of the root of the plant for absorption.It is considered that adsorbed ingredients of fertilizer are converted chemically and/or bio-chemically of the plants following first-order reaction kinetics. The diffusibility of the nutrients to the soil by mass transport. So, the no of molecules of water transported to the soil is represented as:
+
The flux at any time and position for chemical and bio-organic fertilizers are
(chemical fertilizer)and (bio-organic fertilizer).This shows that the developed biofertilizers as compared to the chemical fertilizers show better results in terms of dissolution rate and absorption capacity.
