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In this study, we introduce a novel multi-scale Pore Network Model (PNM) designed to couple reactor-scale and particle-scale transport phenomena. To model reactor-scale phenomena, we employ a 3D reactor-scale PNM. This reactor-scale PNM is extracted from a packed column filled with spherical particles. Through analysis of the reactor-scale PNM, we obtain insight into the flow behavior of the reactor, which, in turn, is utilized for modeling species dispersion. For modeling particle-scale transport phenomena, we employ a 3D particle-scale PNM to simulate species diffusion and reaction within a spherical porous catalyst particle. This particle is represented with thousands of micro-spheres to represent the porous catalyst particles. The developed particle-scale PNM allows the treatment of realistic 3D boundary conditions on the catalyst particle’s surface. This paper presents an innovative methodology by combining the reactor-scale PNM with the particle-scale PNM, achieved through the incorporation of surface fragments. Both the reactor-scale and particle-scale PNMs have undergone thorough calibration and validation in our previous research (Fathiganjehlou et al. 2023; 2024). The developed multi-scale PNM offers a fast model capable of generating local partially resolved results for the catalytic packed bed reactor within a matter of minutes. This model lays the foundation for multi-scale pore network modeling of real packed bed reactors.

In this paper, Magnetic Resonance Imaging (MRI) and a Pore Network Model (PNM) are used to characterize the flow in packed beds of spherocylindrical particles. PNM is chosen as it is a relatively fast numerical approach, which provides local information on the bed flow pattern. MRI scans of packed bed reactors provide detailed information on the bed structure and the flow. In this study, the packed beds are reconstructed from the MRI images. The impact of the image quality on the PNM’s flow field prediction is assessed. It is shown that improved image quality significantly enhances prediction accuracy. With a sufficient image quality, PNM is able to closely match MRI in predicting the flow fields and capture important characteristics such as wall channeling.

In this work, the hydrodynamics inside packed beds of particles with different shapes are investigated: spherical, cylindrical, and cubical particles. The cylindrical and cubical geometries contain sharp ridges, which give rise to complicated pore geometries. In this study, Pore Network Modeling (PNM) validated with the Particle-Resolved Computational Fluid Dynamics (PR-CFD) simulations of packed beds with these non-spherical particles will be reported. The results show that the PNM predicts the same average flow behavior and pore pressure variations as PR-CFD. However, the PNM prediction of the pressure values is less accurate at the pore level compared to the PR-CFD for the cubical particles.

Multitubular reactors are commonly used in industry for processes involving highly exothermic chemical reactions. This reactor type consists of individual tubes, with a small diameter compared to the particle size. These slender beds facilitate heat management, but also give rise to flow maldistribution, which decreases the reactor efficiency. The aim of this article is to validate particle-resolved simulations using Magnetic Resonance Imaging experiments while focusing on the flow maldistribution. The packing structure used in the simulations is reconstructed from the experimental images to facilitate a one-to-one comparison. A good match between experiments and simulations is found for the averaged flow profile, probability density function of the velocity in axial direction and even the local velocity distributions. However, a correction of the experimental results for magnetic susceptibility artifacts is necessary to obtain a similar match in the probability density functions and the local profiles.

Trickle bed reactors (TBR) are widely used in the chemical industries. These reactors involve gas and liquid flow through a catalyst-packed bed. For optimal TBR performance, it is crucial to achieve a uniform distribution of gas and liquid among the catalyst particles. However, in multitubular reactors with slender tubes, flow maldistribution near the tube walls is a common issue. Therefore, a comprehensive understanding of local phase and flow distribution is essential for designing and operating reactors with slender tubes. This article employs Magnetic Resonance Imaging (MRI) to characterize the three-dimensional distribution of the two-phase trickle flow within a slender tube. Three quantities are characterized: gas-liquid-solid distribution, particle wetting efficiency, and the flow field. Structure and flow MRI images are processed to calculate these quantities. Additionally, a novel postprocessing technique is introduced to determine the liquid distribution over individual particle surfaces. This distribution is determined at several axial and radial positions.

Fluidized beds are commonly applied to industrial drying applications. Modeling using the computational fluid dynamics-discrete element method (CFD-DEM) can be employed to increase the fundamental understanding of solids drying. A large drawback of CFD-DEM is the computational requirements, leading to a limitation regarding the system size. Coarse-grained CFD-DEM is an approach to reduce computational costs, allowing one to simulate larger fluidized beds. In this article, coarse-graining CFD-DEM scaling laws are used for fluidized bed solids drying. Three superficial gas velocities are investigated. The particle temperature and density are accurately described. Besides, the Sherwood number is well captured by the coarse-graining simulations.

The distribution of catalytically active species in heterogeneous porous catalysts strongly influences their performance and durability in industrial reactors. A drying model for investigating this redistribution was developed and implemented using the finite volume method. This model embeds an analytical approach regarding the permeability and capillary pressure from arbitrary pore size distributions. Subsequently, a set of varying pore size distributions are investigated, and their impact on the species redistribution during drying is quantified. It was found that small amounts of large pores speed up the drying process and reduce internal pressure build up significantly while having a negligible impact on the final distribution of the catalytically active species. By further increasing the amount of large pores, the accumulation of species at the drying surface is facilitated.

The distribution of catalytically active species in heterogeneous porous catalysts strongly influences their performance and durability within industrial reactors. A drying model for investigating this redistribution is developed and subsequently the impact of non-linear couplings of liquid viscosity and surface tension on hydrodynamics and redistribution of species during the drying process investigated. The gained insights are then used to exert control of the redistribution within the presented model by solely varying external process parameters.

The diffusive fluxes in porous media are inherently influenced by a reaction occurring at the internal surface. This investigation analyses this impact via a Fourier-mode analysis in a spherical coarsely porous model geometries consisting of random agglomerates of spheres. Trends are determined from the results and the overall impact for the given geometries estimated.

Dispersion is the spreading of a solute while it is moved by a flowing medium. The study of dispersion in catalytic chemical reactors is fundamental to their design, since dispersion influences the reactant and product transport within the bed. In this paper, longitudinal and transverse dispersion of an inert tracer in slender packed beds of spheres and spherocylinders is studied using Computational Fluid Dynamics simulations. The focus is on the analysis of dispersion from full field data. The purpose is to develop a methodology that can later also be used to characterize dispersion from full field experimental data such as MRI measurements. Results obtained by means of particle-resolved CFD simulations are discussed. Spatial distributions and residence times are analyzed and the results are interpreted by comparison to results obtained from 1D and 2D convection-diffusion equations