Novel Multiplicity and Stability Criteria for Non-Isothermal Fixed-Bed Reactors

With the increasing need to utilize carbon dioxide, fixed-bed reactors for catalytic hydrogenation will become a decisive element for modern chemicals and energy carrier production. In this context, the resilience and flexibility to changing operating conditions become major objectives for the design and operation of real industrial-scale reactors. Therefore steady-state multiplicity and stability are essential measures, but so far, their quantification is primarily accessible for ideal reactor concepts with zero or infinite back-mixing. Based on a continuous stirred tank reactor cascade modeling approach, this work derives novel criteria for stability, multiplicity, and uniqueness applicable to real reactors with finite back-mixing. Furthermore, the connection to other reactor features such as runaway and parametric sensitivity is demonstrated and exemplified for CO2 methanation under realistic conditions. The new criteria indicate that thermo-kinetic multiplicities induced by back-mixing remain relevant even for high Bodenstein numbers. In consequence, generally accepted back-mixing criteria (e.g., Mears' criterion) appear insufficient for real non-isothermal reactors. The criteria derived in this work are applicable to any exothermic reaction and reactors at any scale. Ignoring uniqueness and multiplicity would disregard a broad operating range and thus a substantial potential for reactor resilience and flexibility.