Taylor's Dispersion in Stratified Porous Media

Abstract

Abstract 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, gives 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.