Analytical quantification of coefficients in the Ergun equation for fluid friction in a packed bed

A new analytical derivation for momentum transport during laminar flow through granular porous media is discussed and some of its implied results described. In the very low Reynolds number regime fully developed laminar flow is assumed and in the higher laminar Reynolds number regime the Forchheimer (non-Darcy) effect is modelled through reference to form drag induced by the solid constituents of the porous medium. The results are compared to the Ergun equation, which is empirically based on experimental measurements, and the correspondence is shown to be remarkably close.