Kinetic studies of the urease-catalyzed hydrolysis of urea via a nonlinear reaction-diffusion model

Biochemical urea hydrolysis, catalyzed by the enzyme urease, is the basis for most electrochemical urea biosensors, utilizing the conversion of urea into ammonium and carbon dioxide. A mathematical model is discussed for urea degradation catalyzed by free acid urease, with relevant to electrochemical and biochemical reaction–transport systems. The model describes urease-mediated urea hydrolysis associated with enzyme-induced carbonate precipitation through a nonlinear reaction-diffusion equation. The governing formulation incorporates a Michaelis-Menten–type nonlinear reaction term to capture enzymatic saturation effects, coupled with source–sink contributions arising from mass transport and reaction processes. The influence of key kinetic and transport parameters on urea conversion is systematically examined over a wide parametric range. A unified Akbari-Ganji method is employed to obtain accurate analytical expression of concentration of urea beyond the limitations of classical Michaelis-Menten kinetics, including the effects of all parameters. The Effectiveness factor also validation demonstrate the robustness of the proposed model. The results provide mechanistic insight into nonlinear electrochemical-biochemical interactions and highlight the potential of enzyme-assisted processes for sustainable electrochemical and bio-electrochemical applications.

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