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

Abstract

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.

Nonlinear Behavior of Methanol Synthesis Compared to CO2 Methanation

“…A similar approach was proposed by Bremer and Sundmacher [7] for the methanation reaction based on conversion rather than heat production. The present approach based on heat production is more suitable for multireaction systems like methanol synthesis but will be also applied to methanation to provide a direct comparison of the two reaction systems and elucidate the differences in behavior.…”

“…Further, it was argued, since CO formation via the reverse water-gas shift reaction (3) is endothermic, in principle, the amount of CO increases with rising temperature, but it was shown that the amount of CO is negligibly small at temperatures below 500°C [7,12], so that reactions (1) and (3) can be neglected for a pure H 2 /CO 2 feed. Another important aspect of CO 2 methanation is catalyst deactivation [13], which is, however, beyond the scope of this work and therefore not considered in this paper.…”

“…Another important aspect of CO 2 methanation is catalyst deactivation [13], which is, however, beyond the scope of this work and therefore not considered in this paper. An important aspect of CO 2 methanation, which is highly relevant for this paper and will be illustrated below, is the fact that CO 2 conversion, and therefore also the heat production of the chemical reaction, increases with rising temperature in the relevant range of operating conditions [7].…”

“…An analytical calculation of the heat production is not possible anymore, due to the highly nonlinear concentration and temperature dependence of the reaction rates. Instead, a semianalytical approach is proposed, where the heat production is evaluated for different temperatures by a numerical solution of the material balances (7), (8) and substituting the solution into Eq. ( 9).…”

“…Typical examples are polymerization reactions [3], some homogeneously catalyzed liquid phase (e.g. [4,5]), and heterogeneously catalyzed gas phase reactions, like H 2 oxidation [6] or CO 2 methanation [7]. The latter has gained a lot of interest during the last years, in the framework of novel power-to-X concepts.…”