Flow in Packed Tubes with a Small Tube to Particle Diameter Ratio
A computer-generated slim tube randomly packed with spheres of almost uniform size is used to model single-phase flow in a packed tube with a small tube diameter to particle diameter ratio, R. To obtain a detailed description of its morphology, the slim packed tube is first tessellated into tetrahedra in the interior, and pentahedra near the walls of the tube. Then, the pore space is represented by a network of interconnected circular and triangular sinusoidal flow channels. The size and length of each channel, as well as their interconnectivity, are exactly known. In addition, porosity and solid surface area per unit volume of the porous medium are determined as a function of distance away from a wall. These data suggest that the presence of the walls has two counteracting effects on fluid flow. A higher porosity promotes flow along the walls but a higher surface area per unit volume hinders it. To confirm this prediction, experimental permeability data are obtained for tubes with R between 2.5 and 40. For R > 25, the permeability is the same as that of a large diameter tube, k,. Between 8 and 25, the permeability can be larger or less than k,. The way the tube is packed determines whether the higher porosity or surface area dominates in the wall region, and thus higher or lower permeability. Below R = 8, the confining walls cause a marked increase in overall bed porosity and the permeability is always larger than k,. Theoretical predictions of the permeability of such very slim tubes are in good agreement with experimental data.