The law of additive reaction times in fluid-solid reactions

Abstract

A law governing the rate of reaction of a solid particle with a fluid is proposed and verified for a wide range of systems. It is exact for the reaction of a nonporous solid and is a useful approximation in the case of a porous solid. The law states that the time required to attain a certain conversion is the sum of the time required to reach the same conversion in the absence of resistance due to the intrapellet diffusion of fluid reactant and the time required to reach the same conversion under the control of the intrapellet diffusion. The limitations are that the solid should be isothermal, the intrinsic kinetics should be at least approximately of first order with respect to the concentration of fluid reactant, and the effective diffusivity should remain unchanged during the reaction. Furthermore, with the appropriate definition of the fluid-solid reaction modulus, numerical criteria for asymptotic regimes of chemical reaction and diffusion controls have been shown to remain identical for all systems considered. The law is valid not only in an integral (conversionvs time) form but also in a differential form: The rate of reaction at a certain conversion can be obtained from the differential form of the law. The latter is valid even when the bulk temperature and concentration vary with time, which makes it possible to apply the solution directly to multiparticle systems such as packed-bed, moving-bed and fluidized-bed reactors.