Numerical modeling of complex two-level masstransfer in media of microporous particles taking advantage of the Crank-Nicolson method
Journal Title: Вісник Тернопільського національного технічного університету - Year 2015, Vol 80, Issue 4
Abstract
Numerical solution for mathematical model of two-component diffusion in catalytic porous particles media has been proposed. The work is based on the results of previously proposed bi-porous model and considers diffusion in micro- and nano porous particles, as well as diffusion in intraparticle space of catalytic media. More over, this model takes into account diffusion of competition, when more that one component can be adsorbed. Proposed model consists of a system of two partial differential equations, the first equation deals with diffusion in intraparticle space, the second equation describes diffusion inside porous particles and the interaction between equations are described as boundary conditions. Solution for two-component competitive diffusion mathematical model was obtained taking advantage of the Crank-Nicolson approximation method. The resulting solution was the basis for calculation algorithms construction and was applied for numerical simulation of graphical dependencies of component concentrations inside particles and intraparticle space of media. Numerical simulations of two components diffusion process flow over the time depending on various characteristics of the catalytic media, including diffusion coefficients of diffusing components have been performed. The resulting model profiles of concentration in interparticle space in time allow to estimate the dynamics of concentration changes in particle for various positions in the zeolite. Thus for particles that are in the top layer of the media concentration increases more rapidly and almost immediately reaches the state of saturation. At the same time, with the movement deep into the media, concentration profiles become more gentle, but eventually also reach the state of equilibrium. Considering concentration inside the particles, it is worth noting that the lowest concentrations are observed in its center and they increase while moving from the center to the outer surface of particles. Moreover, the outer surface of the particles concentration value is equal to the concentration value in the interparticle space. Besides more rapid growth of the concentrations dynamics for the second component of a two-component diffusion was noticed, caused by the higher value of its kinetic characteristics.
Authors and Affiliations
Mykhaylo Petryk, Dmytro Mykhalyk, Maria Petryk
Keywords
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