Speaker
Description
Porous reactors and multiphase systems are ubiquitous in chemical engineering, spanning packed-bed catalysis, coated monoliths, foam catalysts, membranes, and electrochemical devices. In these systems, macroscopic performance is governed by the close relationship between the intrinsic kinetics and transport phenomena occurring across widely separated length scales: advection, dispersion, and mixing at the reactor scale coexist with diffusion, and surface reaction within complex microstructures (pores, tortuous pathways, and reactive internal surfaces). Resolving the full pore-scale physics in three dimensions can capture these effects, but the computational cost is typically prohibitive for reactor-scale design, optimization, and uncertainty analysis.
Homogenization via multiple-scale expansion provides a rigorous route to bridge micro- and macro- scales without sacrificing the essential impact of the microstructure. Starting from pore-scale advection–diffusion–reaction (ADR) equations, the method derives an upscaled, continuum description in which the detailed geometry is accounted in effective transport and reaction coefficients. In the resulting macroscopic model, quantities such as effective dispersion tensors, corrected convective fluxes, and effective reaction source terms encapsulate the influence of porosity, tortuosity, and internal surface area. These coefficients are introduced by solving well-posed cell problems on a representative, periodic volume element.
The mathematical method guarantees that, when the characteristic macroscopic length of the domain ($L$) is much larger than the characteristic size of the microscopic unit cell ($l$), the upscaled model is significantly more computationally efficient than the pore-scale description, while introducing a controlled approximation error that scales with the degree of scale separation, ($err=\mathcal{O}(l/L)$). Because this condition is often satisfied in chemical reactors, where particle-scale features are typically orders of magnitude smaller than the reactor dimensions, the homogenized formulation provides a fast yet accurate alternative for reactor-scale simulations, enabling extensive parametric studies and design optimization that would be impractical with fully resolved pore-scale models.
For demonstrating the accuracy of this technique, we consider a packed bed reactor consisting of solid particles immersed in a continuous liquid phase. A heterogeneous reaction takes place at the liquid–solid interface, where a dissolved solute from the liquid phase is consumed. We generated the periodic unit cell that will compose the macroscopic domain in COMSOL Multiphysics, and we solved the closure problem to evaluate the effective coefficients, such as permeability and dispersion tensor. Then we built the pore-scale model and the corresponding full homogenized one and we evaluated the average concentration along the flux direction. We tested the model under several operating conditions, and we evaluated the applicability range of dimensionless numbers in which the full-homogenized model is comparable to the pore-scale one.
| Country | Italy |
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