Flow of fluids through granular material: Filtration, expansion, and hindered settling

Abstract

Investigations of the flow of fluids through granular materials generally have been limited to such studies as filtration, ground‐water movement, flow of gases through packed columns, etc., in which the fluid passes through an assemblage of stationary particles. There are however, at least two other phenomena often encountered in engineering practice which appear in be essentially identical to filtration but which have received little or no fundamental consideration (The term, filtration, as used throughout this paper designates a condition of flow.) Those are commonly referred to as “expansion”, in which the particles are suspended in an upward‐flowing fluid while the particle‐column as a whole is stationary, and “hindered settling”, in which the particles settle in the fluid with a uniform terminal velocity while the fluid‐column remains stationary. In each of these three cases of the general problem of flow through granular materials, the factors which influence the resistance to flow, namely, velocity, particle‐size, density viscosity, and porosity, are essentially the same; hence, a single equation should satisfy the requirements of all three cases.

Fluidization of an Anthracite Coal

“…Fluidization as now applied to catalysis is characterized by countergravity flow of gaseous fluids through beds of fine, solid particles. In an analysis of pressure drop-fluid velocity relations of such systems, it has been observed by various investigators (6,9, IS, 15,16) that the bed begins to expand at a definite fluid velocity. Although the pressure drop increases steadily with the fluid velocity for flow through unexpanded solids, it remains essentially constant for flow through expanded materials.…”

Pressure Drop Due to Vapor Flow through Moving Beds

“…Blake (3) and others (8, 13, 30), using this method of correlation, assumed that resistance to flow could be expressed by an analogy to Poiseuille's law in which the average diameter of the passages flow of fluid was expressed in terms of a modified hydraulic radius. Fair and Hatch (13,24,25) presented a general modification of this type of correlation and applied it to nonuniform packing, using the reciprocal mean diameter. Leva (35,36) employed a similar fractional void volume function but used a different method for obtaining average diameter than Fair and Hatch. Chilton and Colburn (9) considered that since pressure drop through a bed consists to a major extent of expansion and contraction losses, it should not be correlated on the basis of flow in capillaries.…”

“…A number of studies have been conducted also in the closely related field of fluidization, where the particles no longer move uniformly as in the case of moving beds and sedimentation. Earlier references include fluidization in solid-liquid systems (23,25,27). Several recent publications deal with the fluidization of solid-gas systems (37, 45,55), but it appears that an exact approach to the general problem is difficult.…”