The purpose of this research is to develop a new method to deal with packed-tube reactors where the tube to particle diameter ratio is small. Such reactors are widely used in industrial applications for difficult to control exothermic reaction. The PI is developing a novel approach using the microscopic conservation equations to model the interaction of the transport processes with the rates of reaction. The technique involves formal solution of the overall equation combined with experimental work to provide the needed parameters. In the final analysis, a numerical technique emerges which can be adjusted for accuracy by changing grid sizes. Coarse grids allow fast simulations even for large packed beds - fine grids allow particulate resolution where this is desired.