Chemical Engineering Science, Vol.207, 280-304, 2019
Effects of correlated morphological and topological heterogeneity of pore network on effective transport and reaction parameters
The effective diffusivity and the effective Thiele modulus of reactive porous matrices are determined by using a hybrid discrete and continuum model. The model describes static heterogeneity with weak noise on both morphology and topology of the matrix. Variations in diffusivity with respect to pore size (radius and length) and network connectivity up to second order are analyzed to assess the effect of stochastic media on catalytic reaction and transition of a single species. The porous medium is simulated by several building blocks (BB) which are regular in topology and morphology. A methodology is presented to construct a BB such that it fits the true matrix. Permutation of several regular pore networks in series constructs the porous media. Local mass balances over each BB yields model equations for reaction and transport in the matrix. Correlated random walk theory is used in each BB in order to relate the diffusivity to the coordination number. The Gaussian correlation function is assumed to model the autocorrelation of independent variables which are used to characterize the correlated porous media. The contribution of the fluctuating parameters in the mass conservation of the matrix yields a new closure equation in which ensemble average concentration of the reactant depends on different cross-correlations. The model is stable as long as the Thiele modulus at the correlation length scale is small. It predicts that geometrical heterogeneities lead to correction in effective diffusivity while the reaction rate is unaffected due to small Thiele modulus at correlation length scale. The model is verified by assessing the Thiele modulus of a pore network under Knudsen regime during a first order catalytic reaction; a good agreement was found especially for moderate Thiele modulus of correlated network. However, it fails to simulate random networks. Our systematic study revealed that the pore radius statistics impact significantly the diffusivity and the Thiele modulus while the topological parameters are important in weakly connected networks. The model predictions show that the diffusion constant decreases sharply as pore radius variance increases but increases smoothly with Thiele modulus. (C) 2019 Elsevier Ltd. All rights reserved.