A simplified mathematical model describing the activation of carbon

Abstract

In this paper we have attempted an investigation of the activation of a single carbon particle, assumed to be spherical, in which the steam gasification reaction occurs. The particle is initially filled with steam at a given partial pressure and the reaction starts at a desired temperature at time zero. We also suppose the reaction to be isothermal and the steam concentration at the outer surface of the sphere to be constant. The equations describing the water concentration in the pore volume and the increasing pore radius are a pair of coupled, nonlinear differential equations. We submit some analytical results, qualitative behaviour and uniqueness aspects. Owing to its nonlinearity, the system of equations was solved using a difference scheme. Pore growth data are available in the form of dimensionless plots for particle radii of 0.15 cm and 0.015 cm at different temperatures and partial pressures of steam. In the larger particle the reaction rate is diffusion limited and the pore radius of the activated particle increases from the centre to the outer surface of the particle. In the smaller particle the reaction is in the kinetic region and pore size is almost constant within the particle. The resultant pore size distribution is thus more favourable with the smaller particle.