Multiscale modeling of packed-bed microwave reactors and estimation of intrinsic materials' permittivity
Modeling of packed-bed microwave reactors relies on an accurate representation of particle size, shape, and distribution within the bed, as well as the particles' dielectric properties. The measured permittivity of microwave susceptors (powders or structured materials) depends on the geometric features of the particles and the porosity of the bed, as well as the specific form factor of a structured material. These are effective properties and cannot be used to analyze other reactor configurations unless the geometric effects are removed. Therefore, we introduce a methodology for extracting the intrinsic particle permittivity from experimentally measured effective permittivity by combining cavity-based measurements with multiscale simulations and machine learning. Further, we develop the first multiscale model of packed-bed microwave reactors that incorporate particle effects (geometric features, random packing, and particle contact). This approach bridges macroscopic observables with mesoscopic physics, enabling analysis of local hotspots, arcing, and contact effects that control reactor performance. Using polymer-based spherical activated carbon (PBSAC) and silicon carbide (SiC) as examples, we demonstrate that the inferred particle permittivity is consistent with independent experimental heating profiles we collect from microwave reactors without adjustable parameters. Finally, this methodology establishes a foundation for predictive, multiscale design of microwave packed-bed reactors that explicitly accounts for particle-scale effects, enabling the estimation of intrinsic permittivity for the first time.