A new model for granular porous media: Part I. Model formulation

Abstract

A new model for porous media comprised of monosized, or nearly monosized grains, is developed. In applying this model to a packed bed, the bed is assumed to consist of a series of statistically identical unit bed elements each of which in turn consists of a number of unit cells connected in parallel. Each unit cell resembles a piece of constricted tube with dimensions which are random variables. The problem of flow through each unit cell is reduced, subject to reasonable assumptions, to the determination of the flow in an ALKlVlADES C. PAYATAKES CHI TlEN and RAFFI M. TURIAN infinitely long periodically constricted tube. The solution of this flow problem is given in a companion publication. This model, together with the solution of the flow through it, can be used for the modeling of processes which take place in the void space of a bed.As a preliminary test, theoretical friction factor values, based on the proposed model, were compared with experimental ones for two different beds and found to be in good agreement even in the region of high Reynolds numbers where the nonlinear inertia terms are significant. SCOPEThe main purpose of this paper is to present a new model for porous media of the type represented by randomly packed beds of monosized, or nearly monosized, grains. The model has been developed as a first step in

The creeping motion of immiscible drops through a converging/diverging tube

“…andRe defined in terms of rHP· Data for the wavy-wall tube expressed in terms ofj andRe are shown in figure 3; they coincide precisely with the Hagen-Poiseuille law for a straight-wall tube with radius rffp, thus demonstrating the relevance of rHP as a lengthscale of the flow under present conditions. Detailed velocity and pressure fields for flow through periodically constricted tubes of a variety of shapes have been calculated by Payatakes, Tien & Turian (1973), Payatakes & Neira (1977), Neira & Payatakes (1979), Fedkiw & Newman (1977), Deiber & Schowalter (1979) and Payatakes & Tilton (1983). These results consistently show that a log-log plot of an appropriately defined friction factor versus Re yields a linear relationship as shown in figure 3, at least up to the value of Re at which either flow separation or turbulence occurs.…”

Thermal conductivity of granular porous media: A pore scale modeling approach

“…Network modeling technique qualitatively, within an order of magnitude, predicts some petrophysical parameters such as permeability for sand packs and sandstones. [30][31][32][33][34] However, its application for the quantitative predictions of petrophysical properties has been challenging because this method is based on some assumptions that oversimplify a real structure of void spaces. For instance, at each site, a particular value is assigned to the number of bonds; or throats are assumed to have the same length.…”

Flow in packed tubes with a small tube to particle diameter ratio

“…It should be mentioned that numerous analyses for flow through sphere packs exist. There are solutions for flow in regular sphere packs (Snyder and Stewart, 1966;Sgrensen and Stewart, 1974;Zick and Homsy, 1982;Lahbabi and Chang, 1985), for models with flow over a single sphere (Neale and Nader, 1974), and for models with flow in a constricted channel between spherical particles (Payatakes et al, 1973;Payatakes and Neira, 1977). None is available for an actual random sphere pack, not to mention one with the wall effect present.…”