PREDICTING EFFECTIVENESS FACTOR FOR M-TH ORDER AND LANGMUIR RATE EQUATIONS IN SPHERICAL COORDINATES

The effectiveness Lctor is widely used to account for the interaction between pore diffusion and reactions on pore walls in porous catalytic pellets and solid fuel particles. The effectiveness factor is defined as the ratio of the reaction rate actually observed to the reaction rate calculated if the surface reactant concentration persisted throughout the interior of the particle, Le., no reactant concentration gradient within the particle. The reaction rate in a particle can therefore be conveniently expressed by its rate under surface conditions multiplied by the effectiveness factor. The generalized steady-state equation in a spherical particle (a catalytic pellet or a solid fuel particle) may be, expressed as: d2C 2 dC r”’ -+----=o dr2 r dr D, where r”’ is the intrinsic reaction rate per unit particle volume in moL’cm3/sec (as a function of C), D, is the effective diffusivity, C is the local oxygen concentration (as a function of r), and r is the radial distance from the origin. The boundary conditions are C = C,, at r = r, (2)