Parabolic profile approximation (linear driving-force model) for chemical reactions

• Published in: Chemical engineering science 1990, Vol.45 (2), p.443-448
• Main Authors: Goto, Motonobu, Smith, J.M., McCoy, Ben J.
• Format: Article
• Language: English
• Subjects: Chemistry; Exact sciences and technology; General and physical chemistry; Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/0009-2509(90)87030-V

The parabolic approximation for the concentration profile inside a particle yields a substantial simplification in computations. The linear driving-force model for combined internal diffusion and external mass transfer arises from the approximation. We have applied this approximation to consider the time dependence of two cases of isothermal, irreversible, first-order chemical reaction in a spherical particle and in a slab: (1) when the reactant is a nondiffusing (adsorbed or solid) component initially inside the particle and the products diffuse out of the particle (e.g. for a reaction extraction), and (2) when the reactant is diffusing into the particle (e.g. for a catalytic reaction). The approximation is found to be satisfactory over a wide range of parameters for case (1). For case (2), however, the accuracy of the approximation is limited to small Biot numbers and Thiele moduli.