(82e) Bifurcation Analysis for Allothermic High-Temperature Pyrolysis of Methane in a Moving-Bed Reactor

Multiple steady states are known for numerous reaction engineering examples involving exthermic reactions e.g. in moving bed reactors or reverse-flow reactors. This paper reports studies on the bifurcation analysis and the generation of regions of multiplicity in the operation of moving-bed reactors. The studies were first carried out for a generalized model, which allows the investigation of the effect of various scenarios, such as changes in heat capacity or the number of moles with reaction, as well as the previously unstudied equilibrium and allothermic reactions. Based on these the insights gained from this extension were then applied to an actual reaction, namely the high temperature pyrolysis of methane.

The study of the high temperature pyrolysis of methane is motivated by the search for alternatives to produce hydrogen with low to zero carbon dioxide emissions. Among them, the decarbonization of the fossil energy, especially the high temperature methane pyrolysis, constitutes a promising drop-instrategy. To assess its potential, a research program has been set up to develop a novel two-step process for first generating hydrogen and carbon and then using the former to produce synthesis gas utilizing carbon dioxide. To carry out the pyrolysis of ethane, the moving-bed reactor represents a promising approach, since it has been successfully operated at high temperatures in the metallurgical industry and elsewhere.

The standard models for a moving-bed reactor with a heterogeneous reaction can be easily derived from differential balances under the usual assumptions of negligible axial and radial conduction and diffusion, plug flow in both the solid and gas phases, and temperature-independent properties. The steady-state dimensionless model equations describing a mass and two energy balances for the gas an solid phase. In this work, a generalized dimensionless model for a moving-bed reactor was developed and the influence of several parameters was investigated. The parameter found to have the greatest influence on the multiplicity behavior was the Stanton number. In addition, cases for systems exhibiting changes in moles and heat capacities were studied, showing a larger influence than would have been predicted a priori, mainly because they show the highest influence on the Stanton number.

Furthermore, the insights gained from the generalized model were applied to the allothermal operation of the high-temperature pyrolysis of methane. Here, the reverse reaction at higher pressures was identified as possible source of multiplicity due to its exothermicity. In addition, for a nonlinear heat input it could be shown that multiple steady states can be found for particular cases. The interaction of these two effects was demonstrated in a heat-integrated reactor.

In general, although the case studied was not ideal, the results obtained could be used to show the existence of multiple steady states in other allothermal systems, where the coupling of the reaction and the nonlinear heat input occur in a narrower temperature range as can be seen from the shifted temperature curves.

Finally, the bifurcation methods proved to be a valuable tool when performing parameter studies, and although, depending on the complexity of the system, the simulation can demand considerable computational effort, a more refined coding or the introduction of the Jacobian matrix would dramatically improve the performance.