MATHEMATICS

Mathematical modeling of industrial ammonia synthesis using nonlinear reactiondiffusion equations

J. Khasanov^a, S. Yu. Muminov^b, S. B. Iskandarov<sup>c

a</sup> Urgench State Pedagogical Institute, Urgench 220100, Uzbekistan
^b Mamun University, Khiva 220900, Uzbekistan
^c Urgench State University named after Abu Rayhan Biruni, Urgench 220100, Uzbekistan

Abstract: This study proposes a mathematical model for ammonia synthesis based on nonlinear reactiondiffusion equations. The model integrates degenerate gas diffusion in the reactor with Haber-Bosch reaction kinetics to explore efficiency and environmental sustainability. A theoretical analysis is conducted to establish the existence and stability of global solutions for the underlying degenerate parabolic system. Numerical simulations were validated against industrial data from Navoiyazot facility in Uzbekistan, demonstrating 98.2% accuracy in concentration profiles and outperforming constant-diffusivity models by 12–15% in low-concentration regions.

Keywords: nonlinear reaction-diffusion, degenerate diffusion, ammonia synthesis, Haber–Bosch kinetics, global stability.

Received: 04.11.2025
Revised: 20.11.2025
Accepted: 23.11.2025

Language: English

DOI: 10.17586/2220-8054-2025-16-6-749-754