AN ASYMPTOTIC MODEL FOR GAS-SOLID FLOW IN A COUNTERCURRENT MOVING BED REACTOR

Asymptotic methods are employed to analyze earlier two-phase steady-state Euler-Euler models that were originally intended as simplified representations for gas-solid flow in an ironmaking blast furnace; more generally, however, they can be thought of as models for two-phase flow in countercurrent moving bed reactors. A scaling analysis, based around the fact that the solid velocity is typically several orders of magnitude smaller than the gas velocity, indicates that the effects of viscosity and inertia are basically negligible compared with those of gravity and interphase momentum transfer. The resulting reduced model yields quasi-analytical expressions for the solid fraction and the gas velocity, with the former being directly related to the shapes of the reactor and any stagnant zone that may form as a consequence of solids or granular materials being able to withstand substantial amounts of shear; in ironmaking blast furnaces, this occurs near the bottom of the reactor, and the zone is commonly known as the deadman. On the other hand, the solid velocity can be found via a numerical solution of Laplace’s equation; nevertheless, the solution is different to that obtained from earlier potential flow models in blast furnace modeling. Most significantly, the current model would form the basis of a computationally efficient approach for modeling transient heat and mass transfer with chemical reactions in a countercurrent moving bed reactor.