Bifurcation Analysis of Homogeneous-Heterogeneous Combustion

We present theory and comprehensive bifurcation analysis of thermally coupled homogeneous-heterogeneous combustion of propane and methane in short monolith, fibermat or gauze type reactors with a focus on the dependence of the ignition, extinction, hysteresis, double and boundary limit loci on the various design and operating parameters. We analyze the impact of inlet fuel mole fraction, inlet temperature, residence time and channel hydraulic radius on the relative position of the homogeneous and catalytic ignition and extinction points and identify the parameter regions in which either catalytic or homogeneous reaction dominates. We also identify the regions in which catalytic ignition leads either to an intermediate branch on which the homogeneous reaction rate is negligible or directly to a high conversion and temperature state thereby facilitating homogeneous ignition. For the case of methane oxidation, we examine both the lean and rich feeds with the operating pressure as the bifurcation variable and compare the predicted results with available experimental data and numerical simulations using detailed CFD models. We then study the impact of the Lewis number, 〖Le〗_f (thermal diffusivity of the reaction mixture to the molecular diffusivity of the limiting reactant) and the Peclet numbers on the maximum temperature attained for coupled homogeneous-heterogeneous combustion process in a parallel plate reactor using one, two and three-dimensional models. For the case of 1-D models, we find that the maximum temperature never exceeds the adiabatic value for physically consistent boundary conditions. For 2-D models, we find that for 〖Le〗_f<1, the hot spot temperature can exceed the adiabatic value, it is always located on the wall and its distance from the inlet and magnitude increase with increasing radial Peclet number. However, for 〖Le〗_f>1, contrary to some literature claims, the peak temperature never exceeds the adiabatic value, though the temperature can be non-monotontic across the channel. We show that 3-D solutions can bifurcate either from 1-D or 2-D solutions irrespective of the value of the Lewis number. The implications of these observations for catalyst and process design in systems in which both homogeneous and catalytic reactions occur are discussed.

Portions of this document appear in: Alam, Imran, David H. West, and Vemuri Balakotaiah. "Bifurcation analysis of thermally coupled homogeneous–heterogeneous combustion." Chemical Engineering Journal 280 (2015): 293-315. DOI: 10.1016/j.cej.2015.05.084. And in: Alam, Imran, David H. West, and Vemuri Balakotaiah. "Transport effects on pattern formation and maximum temperature in homogeneous–heterogeneous combustion." Chemical Engineering Journal 288 (2016): 99-115. DOI: 10.1016/j.cej.2015.11.053.