Taylor's Dispersion in Stratified Porous Media

During 1953-54, Taylor showed that if a certain criterion is met the combined effects of the transverse profile of longitudinal velocity and transverse diffusion on a solvent slowly flowing through a tube will manifest themselves as a longitudinal diffusion phenomenon. A similar phenomenon exists in stratified porous media where the transverse profile of longitudinal velocity and transverse dispersion can produce an effective longitudinal dispersion, called Taylor's dispersion in this paper. Since this effective longitudinal dispersion is larger than the corresponding homogeneous longitudinal dispersion, the quantitative description of this phenomenon would be important to dispersion-sensitive EOR processes, such as surfactant or miscible flooding.Taylor's dispersion will occur in two-layer porous media if a suitably defined dimensionless number is much greater than unity. When this condition holds, the effluent history of a constant-mobility equal-density miscible displacement is that of the same displacement in a homogeneous medium with increased dispersion. The resulting effective longitudinal dispersion may be derived analytically and verified numerically as a function of several media properties. The most important of these are system thickness and permeability contrast.In multilayer media, when two adjacent layers have a large transverse dispersion number they behave as a single layer with suitably averaged properties. This observation suggests an algorithm whereby Taylor's dispersion may be extended to multilayer systems. The algorithm, or grouping procedure, loves effluent histories that are in agreement with numerical solutions to the continuity equation and allow properties of the resulting effective dispersion to be investigated. From the results of this work, Taylor's dispersion can offer an explanation for the large field-scale dispersion observed in tracer test studies. Moreover, it appears that the grouping procedure could indicate a method for obtaining layered reservoir models from core data. Introduction In laboratory displacements, longitudinal (parallel to the bulk fluid velocity) dispersion is well characterized as consisting of additive contributions of diffusion and convection:when K is the longitudinal dispersion coefficient, Do is the molecular diffusion coefficient, F is the formation electrical resistivity factor, v is the interstitial longitudinal velocity, and, is the longitudinal dispersity. At a velocity above about 0.1 ft/D (0.35 mu m/s) the convection term dominates Eq. 1, so for practical displacements about 1 ft/D (3.5 mu m/s) - K depends only on the term, in turn, is a function of average particle size and local heterogeneity, and averages 0.05 to 0.2 in. (0.13 to 0.51 cm) for homogeneous laboratory displacements. Similarly, transverse (perpendicular to the bulk fluid velocity) dispersion iswhen Kt is the longitudinal dispersion coefficient and is the transverse dispersivity. Measurements of are much less common than but they indicate that /30.In the scaled differential material-balance equations, both K and Kt become part of Peclet numbers, vL/K and (vH/Kt)H/L, which appear as inverses in the equations. In laboratory displacements, and are of the order of fractions of centimeters and L is the order of centimeters. SPEJ P. 459^