Two-Dimensional Modeling of a Packed-Bed Membrane Reactor for the Oxidative Coupling of Methane

Oxidative coupling of methane (OCM) represents an opportunity for the replacement of crude oil, which still is the main source for longer hydrocarbons and almost all base chemicals, with natural gas, or biogas. OCM turns methane catalytically into mostly ethylene and ethane. Thus, several different reactor types exist, out of which the packed-bed membrane reactor (PBMR) is one of the most promising given its combination of reaction and product separation in one apparatus and also the improved temperature control because of the gradual feeding of oxygen through the membrane. In previous simulation and optimization studies, one-dimensional models have been used to describe the conventional PBMR. However, due to radial diffusion and thermal conduction those models are not accurate enough. In this work, a two-dimensional model for the CPBMR is presented. Radial diffusion and thermal conduction in the packed-bed as well as in the reactor shell are considered while axial dispersion is neglected. In accordance with experimental studies, Knudsen's diffusivity theory is applied to describe the flux through the membrane. The model is discretized using a combination of Lagrangian and Hermite collocating polynomials on finite elements. The two-dimensional model contains second order derivatives for the radial coordinate. Hence, continuity of both the collocated variable and the first derivative across all finite elements are required in that direction. In this case, Hermite polynomials are advantageous because they allow for the afore-mentioned continuity while negating the necessity of additional equality constraints. As an initial configuration, a length of 20 cm is assumed for the CPBMR with two separate heating/cooling segments of each 10 cm. The tube-side and shell-side diameters are set to 7 and 10 mm, respectively. Preliminary studies have shown that five radial and twelve axial finite elements are required to ensure a stable performance of all optimization studies for the given initial configuration. The resulting large-scale NLP contains more than 130,000 variables. Most fluid properties and transport parameters are implemented as functions of local temperatures and concentrations rather than average values. A brief study shows that their joint influence cannot be neglected. Using La2O3/CaO as a catalyst with kinetics provided by Stansch et al. (1997), an overestimation of more than 25 percentage points can be observed in the yield of C-2 hydrocarbons in a one-dimensional model in comparison to the two-dimensional case. Optimization studies using the solver IPOPT result in operating conditions and reactor configurations with a yield in C-2 hydrocarbons of more than 40 %, which lets the two-dimensional model still appear to be more accurate than any one-dimensional case. However, experimental studies have never shown such a performance at this level. The partial pressure of oxygen in the catalytic packed-bed of the CPBMR will always be comparatively low, usually below 1000 Pa, because of the diffusive flux through the membrane. Most kinetic systems for OCM are derived from micro-catalytic packed-beds and are not meant for this range. Thus, it is still questionable whether current kinetic systems are actually able to accurately describe the behavior.