On the dispersion coefficients for poiseuille flow in a circular cylinder

Abstract

The problem of immiscible displacement of oil ganglia arises in connection with oil bank formation and attrition during enhancwd oil recovery with flooding. A stochastic simulation method is developed here, which enables prediction of the fate of solitary ganglia during immiscible displacement in water-wet unconsolidated granular porous media. This method takes into account the local topology of the porous medium; the initial size, shape and orientation of the oil ganglion and the capillary number. For each ganglion size, hundreds of realizations are performed with random ganglion shapes for a 100 x 200 sandpack. These results are averaged to obtain probabilities of mobilization, breakup and stranding as fudctions of capillary number and ganglion size. Axial and lateral dispersion coefficients are obtained as functions of the average ganglion velocity. The results from the solitary ganglion analysis can he used with the ganglion population balance equations developed in a companion publication (Payatakes, Ng and Flumerfelt, 1980) to study the dynamirs of oil bank formation.

An asymptotic theory for dispersion of reactive contaminants in parallel flow

“…¥= 0 has received scant attention from theorists, despite the importance of boundary reactions (or models of them) in diverse fields such as biology, physiology, chromatography, chemistry and, of course, in environment fluid mechanics. The most notable work, by Sankarasubramanian and Gill [15] and De Gance and Johns [6,7] has been based on the Taylor-Gill approximation…”

“…The cited works [6,7,8,15] are mainly concerned with the /J-dependence of the asymptotic forms of K 0 (t), K t (t), K 2 {t) at large times. The Taylor-Gill scheme has certain attractive mathematical features as explained by de Gance and Johns, but it is not necessarily the most efficient method at relatively large dimensionless times when a direct large-time 290 N. G. Barton [4] Chatwin style asymptotic expansion may as well be employed.…”

“…The constants A u in (2.9) are then found to be terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0334270000004094 [7] Dispersion of reactive contaminants 293 by fitting the initial condition C x (y, z,0) = S,(j, z), and, after simplification, the full solution for C, is found to be c, = 2 e,//,*-*' 1 + P2 2…”

“…alternative at large times to the Taylor-Gill approach of references [6,7,15]. Accordingly, the variables X, Y, Z and T defined by…”

“…The results are applied in detail to the outstanding practical example-the chemical flow reactor (a device used to measure reaction rates for chemical reactions taking place between fluids). For this case, the paper provides a practical alternative to recent variable diffusion coefficient studies [6,7,15], and presents further results for the concentration distribution and for the limiting behaviour under weak and vigorous reactions at the boundary of the flow. …”