Multiphase reactors constitute a major class of chemical reactors and have proven to be an inseparable part of the chemical industry. Some of the crucial multiphase reactor systems include but are not limited to gas-solid fluidized beds, gas-solid moving beds, and gas-liquid bubble reactors. Chaos analysis is an important and instrumental approach to advance and improve the design and operation of such multiphase reactors. Professor Cor van den Bleek had been the leader of this approach. Specifically, his contributions to the chaos analysis of multiphase reactors have been extraordinary and crucial to characterizing and tuning the operating conditions of the reactor to achieve attractive hydrodynamic regimes that may offer better reactant conversions and product selectivity. The implementation of chaos analysis is predominantly observed in the scale-up studies and the deployment of multiphase reactors in the process industry. The thorough establishment of such fundamental studies has laid a strong foundation for incorporating them into sophisticated predictive methods using machine learning. Using the backbone of such fundamental mathematical studies, we developed a predictive study to understand the drag forces on the solid particles in gas-solid reactors. However, one of the major challenges encountered in the predictive studies of traditional gas-solid reactors is the presence of irregularly shaped solid particles. This presentation describes the machine learning-based approach to modeling a drag force for particles of any irregular shapes in incompressible gas-solid flows. The irregularity of the particle shape is illustrated using the spherical harmonic model. The gas-solid fluidization behavior represented by sparse, poly-dispersed particle-laden flows at low to intermediate particle Reynolds numbers is quantified based on particle-resolved direct numerical simulations (PR-DNS). Specifically, the PR-DNS is utilized to obtain drag force coefficients and flow fields of single particles. A variational auto-encoder model is applied to obtain latent vectors to represent the geometrical features of the particles, with artificial neural networks (ANN) developed to predict drag force coefficients and flow fields of a single particle system. A pairwise interaction extended point-particle (PIEP) model is then applied to obtain the drag coefficients of a single particle in multi-particle systems by assuming the flow fields of individual neighboring particles can be linearly superposed over those of the single particle in consideration. The PIEP and ANN results exhibit moderate correlation and accuracy based on the PR-DNS results. With the PIEP and ANN methods, a steady drag force model is described that does not require heavy data collection for the gas-solid fluidization systems with irregular-shaped particles.
