IMPTECR Algorithm for the Dual-porosity Seepage Model of Ortho-parahydrogen Converter

To explore the heat and mass transfer laws of ortho-para hydrogen catalytic conversion in porous media, this study establishes mass and energy conservation equations for particle pores and bed voids separately based on a dual-porosity medium model. Key physical effects in the conversion process, such as catalytic reaction kinetics and interphase heat/mass transfer, are characterized as source terms in the governing equations, enabling accurate description of complex physical processes in the multi-scale pore structure. Aiming at the core problem in the multiphase seepage system of ortho-para hydrogen converters—significant time-scale differences among the pressure field, temperature field, and component ratio field, with the ortho/para hydrogen ratio field changing sharply and its steep gradient regions easily causing numerical dispersion and oscillations—this study introduces the implicit-explicit stepwise solution idea of the IMPES algorithm and proposes the Implicit Pressure and Temperature-Explicit Component Ratio（IMPTECR） algorithm. Through equivalent algebraic transformation, the algorithm eliminates the time derivative term of the component ratio, and adopts a stepwise strategy of "implicit solution for pressure field-implicit solution for temperature field-explicit solution for component ratio field" to effectively decouple strongly coupled unknowns. Subsequently, the control volume method is used for discretization and numerical solution of the governing equations. Numerical results show that the IMPTECR algorithm exhibits excellent convergence and numerical stability under both adiabatic and isothermal conditions, which can effectively suppress numerical oscillations and error accumulation. Validated against the ortho-para hydrogen catalytic conversion experimental data reported by Hutchinson et al., the model predictions of conversion rate and bed temperature distribution are in good agreement with experimental measurements, confirming the accuracy and reliability of the numerical solution model. This study provides a reliable method for the numerical simulation and optimal design of ortho-para hydrogen conversion systems in porous media.