Modelling mesoporous alumina microstructure with 3D random models of platelets

Pore Network Modeling of Intraparticle Transport Phenomena Accompanied by Chemical Reactions

In this work, a 3D pore network model (PNM) is introduced for modeling reaction-diffusion phenomena, with and without coupled heat transfer, in a spherical porous catalyst particle. The particle geometry is generated by packing thousands of microspheres inside a large sphere to represent the 3D geometry, porosity, and tortuosity of a spherical catalyst particle. A pore-network representation is extracted from this geometry, and a PNM for diffusion-reaction and heat conduction is constructed. This newly proposed particle-scale PNM allows for the application of realistic 3D nonuniform boundary conditions on the particle's surface, which is commonly encountered in slender packed-bed reactors. Concentration profiles inside the particle, and effectiveness of the reactions, is analyzed.

SEM Image Processing Assisted by Deep Learning to Quantify Mesoporous γ-Alumina Spatial Heterogeneity and Its Predicted Impact on Mass Transfer

The pore network architecture of porous heterogeneous catalyst supports has a significant effect on the kinetics of mass transfer occurring within them. Therefore, characterizing and understanding structure-transport relationships is essential to guide new designs of heterogeneous catalysts with higher activity and selectivity and superior resistance to deactivation. This study combines classical characterization via N2 adsorption and desorption and mercury porosimetry with advanced scanning electron microscopy (SEM) imaging and processing approaches to quantify the spatial heterogeneity of γ-alumina (γ-Al2O3), a catalyst support of great industrial relevance. Based on this, a model is proposed for the spatial organization of γ-Al2O3, containing alumina inclusions of different porosities with respect to the alumina matrix. Using original, advanced SEM image analysis techniques, including deep learning semantic segmentation and porosity measurement under gray-level calibration, the inclusion volume fraction and interphase porosity difference were identified and quantified as the key parameters that served as input for effective tortuosity factor predictions using effective medium theory (EMT)-based models. For the studied aluminas, spatial porosity heterogeneity impact on the effective tortuosity factor was found to be negligible, yet it was proven to become significant for an inclusion content of at least 30% and an interphase porosity difference of over 20%. The proposed methodology based on machine-learning-supported image analysis, in conjunction with other analytical techniques, is a general platform that should have a broader impact on porous materials characterization.

Small-angle X-ray scattering intensity of multiscale models of spheroids

The microstructure of heterogeneous catalysts often consists of multiscale aggregates of nanoparticles, some of which are highly anisotropic. Therefore, small-angle X-ray scattering, in classical or anomalous mode, is a valuable tool to characterize this kind of material. Yet, the classical exploitation of the scattered intensities through form and structure factors or by means of Boolean models of spheres is questionable. Here, it is proposed to interpret the scattered intensities through the use of multiscale Boolean models of spheroids. The numerical procedure to compute scattered intensities of such models is given and then validated on asymptotic diluted Boolean models, and its applicability is demonstrated for the characterization of alumina catalyst supports.

Small-angle X-ray scattering intensity of multiscale models of spheres

The different approaches found in the literature to compute small-angle X-ray scattering intensities of stochastic Boolean models from their analytical formulations or their numerical realizations are reviewed. The advantages and drawbacks of the methods for the interpretation of small-angle X-ray scattering curves are investigated. Examples of multiscale models built from union and intersection of Boolean models of spheres and from Gamma or lognormal radius distributions are given. The scattering intensity computed from projections of realizations of such models is compared with the intensity computed from their analytical covariance. It appears that computation from projection induces a strong finite-size effect with a relative constant variance equal to 0.5. Comparison of scattering intensities of an intersection of Boolean model and the corresponding Cox model shows only subtle differences.