Mathematical analysis of the hydrogen–uranium reaction using the shrinking core model for hydrogen storage application

• Reaction of single spherical metallic uranium pellet in hydrogen–helium stream studied.
• No controlling regime assumed beforehand.
• Non-linear reaction kinetics and changing particle size considered.
• Effect of particle size, hydrogen concentration and temperature investigated.
• Ash layer diffusion determined to be rate controlling regime.

The reaction of metallic uranium particles with hydrogen at ambient or above ambient temperature has been used as the basis for the solid state storage of hydrogen in the form of uranium hydride for various applications in the nuclear industry. This work models the reduction of a single particle of metallic uranium to uranium hydride using available kinetic data, the well known shrinking core model and the pseudo-steady state hypothesis. No single rate controlling regime was assumed apriori and the various interfacial gas concentrations were calculated by an iterative procedure as function of the core radius at any time and for given operating conditions. The volumetric expansion or increase in the outer radius of the uranium particle as it is progressively hydrided was also considered in this work. The time required for complete conversion of the pellet to the hydride was then calculated by numerical integration and the rate controlling regime was identified. A spherical geometry was considered in this work for illustrating the technique, but the method is applicable to any kinetic model and any geometry of the pellets after simple modifications to the governing equations.