Identification of scaling law for supercritical water fluidized bed reactors via CFD and data-driven approach

Supercritical water fluidized bed reactors (SCWFBRs) offer significant potential for large-scale hydrogen production, but their scale-up process remains challenging. Traditional scaling laws, such as Glicksman's sets, simplify or omit interphase and interparticle closure terms in conservation equations, limiting applicability under supercritical water conditions. To address this, a data-driven approach is proposed to develop a modified scaling law for SCWFBRs. A dataset was generated from two-fluid model (TFM) simulations across diverse operating conditions and reactor scales. Dimensional analysis, combined with a multi-layer perceptron (MLP) and a pattern search method, was then applied to identify a composite dimensionless number representing interaction closure terms in two-phase momentum equations. This number, together with dimensionless numbers derived from other momentum terms, was refined via XGBoost and backward stepwise feature selection to preserve essential design degrees of freedom, yielding the modified scaling law. Validation against key hydrodynamic indicators, including pressure drop fluctuations, particle volume fraction, and particle axial velocity, demonstrated that the modified law consistently outperforms Glicksman's criteria for both Geldart A and B particles, with the extent of improvement varying between particle types under a tenfold scale-up. These results highlight the importance of accounting for interphase and interparticle interactions in SCWFBRs and indicate that the data-driven approach is an effective tool for reactor design and scale-up.