Diffusion controlled LHHW kinetics. Simultaneous determination of chemical kinetic and equilibrium adsorption constants by using the Weisz-Prater approach

Abstract

A method to simultaneously determine the chemical kinetics (kCT) and Langmuir’s adsorption equilibrium (KL) constants in porous catalyst particles where chemical reactions following Langmuir-Hinshel wood-Hougen-Watson (LHHW) kinetics (first order on the concentration of the adsorbed species) proceed under the existence of diffusion mass transfer limitations was proposed. Two parameters characterize this steady state diffusion-adsorption-reaction system: the well known Thiele modulus / and the dimensionless adsorption equilibrium constant K, which is defined as the product between KL and the fluid phase concentration of the reactant (Cf). It was shown that the non-linear adsorption equilibrium is the reason that, given /, the larger the K, the flatter the concentration profile and, consequently, the volume average chemical reaction rate and the effectiveness factor are higher. Although the Weisz- Prater (W-P) criterion has been previously extended to non-linear kinetics to evaluate the relative magnitude of diffusion limitations inside porous catalyst particles, this method allows determining the kinetic and adsorption parameters by using the W-P parameter, as assessed from a few laboratory experiments. Differently from the classical W-P criterion (first order kinetics), a single value of W-P parameter below which the chemical control could be secured does not exist for LHHW kinetics. Those ‘‘limit” values depend on K and increase with it. The fact that / is independent from Cf , while K certainly depends on it, makes it easier to simultaneously determine KL and kCT under reaction conditions. When K is small (e.g., lower than 0.1), the model converges to the solutions typical in textbooks, where linear adsorption equilibrium is taken into account, which under steady state conditions only allow estimating the kCTKL product, but not the individual constants.