An Investigation into the Laws of Flow of Fluids through Beds of Granular Materials

Abstract

A general equation governing the flow of liquids through a bed of granular material is derived by the use of the method of dimensional analysis. The equation so obtained has been verified by experiment for liquids having absolute viscosities ranging from approximately 16·0 poises to about 0·01 poise, the bed material being spherical shot closely graded about a mean size. Examination of the experimental results shows that the curve relating fluid resistance to Reynolds number has a form very similar to that for a single sphere moving in an infinite fluid, although the discontinuities which are present in the latter curve at the critical value of the Reynolds number are absent in the former; that the effects of the walls of the container are negligible; that the resistance to flow is accurately proportional to depth of bed, and that the hydraulic resistance varies inversely as the fourth power of the voidage of the bed approximately, for beds of normal density of packing, although the value of the index varies with the value of the voidage. The evidence also indicates that the hydraulic resistance is not accurately defined by the mean value of the voidage, but is subject to considerable variations due to the statistical nature of a bed, and that the effect of the walls of the container may be computed on the assumption of flow through a pair of parallel channels of different hydraulic resistance.

A revisit of pressure drop-flow rate correlations for packed beds of spheres

“…(17), (26), (29), (30), (32), (33), and (35) in this paper). The correlation by Hayes, Afacan and Boulanger [46] has been tested with both sets of parameters in this work.…”

“…Considering the data collected by earlier researchers, Carman [10] presented an equation of the Forchheimer type (Eq. (17) in Table 1) and stated that this equation fitted the data best.…”

“…Montillet, Akkari and Comiti [5]; Özahi, Gundoğdu and Çarpinlioğlu [16]) without the porosity correction function h(ε). This porosity correction function was presented in graphical form in another paper by Rose [17] and then given again in graphical form by Rose and Rizk [18] by extending it to higher porosities. Since the h(ε) curve given by Rose and Rizk [18] is very inconvenient to use when a large number of calculations are needed (as is the case in this work), the following curve-fitting polynomial has been developed here to be used (within the range 0.32 b ε b 0.90) in conjunction with the Rose equation: …”

Permeability estimations and frictional flow features passing through porous media comprised of structured microbeads

“…Most of the relations are developed on the basis of capillary models, regarding the flow paths through the pores of a porous medium as capillary tubes or bundles of capillary tubes with equivalent flow features (Ingham and Pop, 1998). However, those relations mostly characterized complex and heterogeneous pore paths by microscopic geometry factors such as grain shapes, roughness and sizes of pores or porous media (Rose, 1945;Achdou and Avellaneda, 1992). Although this seems conceptually reasonable, it is practically impossible because measurement of the size, shape and distribution of a large number of individual grains is not realistic; moreover, the quantification of these factors for the equations would be more challenging (Burmeister, 1993).…”

Extending NMR data for permeability estimation in fine-grained sediments

“…A number of methods exists for estimating permeability from other bulk physical properties. The simplest method assumes a log-linear relationship between permeability and porosity (Rose, 1945), but this relationship varies greatly with lithology and may provide a crude estimate of permeability at best (Neuzil, 1994). Other methods utilize the theory of Kozeny, which states that permeability should be inversely proportional to the square of the specific surface area of the sediment (Kozeny, 1927).…”