Abstract
Abstract A mathematical model is developed to analyze urea hydrolysis in immobilized urease particles. The reaction rate is described by a modified Michaelis-Menten form which takes into account inhibition by ammonium ions and pH-dependent kinetics. The products of urea hydrolysis may exist in several ionic states, which are assumed to be at local equilibrium. A Nernst-Planck diffusion flux expression is used to describe the transport of the charged species, whose diffusivities differ by an order of magnitude. The coupled nonlinear differential equations are solved numerically using orthogonal collocation. Our simulation results indicate that at a bulk urea concentration less than KM (Michaelis-Menten constant), the effectiveness factor approaches that for product-inhibited Michaelis-Menten kinetics. At higher urea concentrations, the reaction rate of urea hydrolysis within a single particle is dominated by the pH dependence of the kinetics. Ionic equilibria of the product species cause the solution pH to...
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