Dispersion and Reservoir Heterogeneity

Abstract

Summary Macroscopic dispersion is the mixing, on the scale of several hundreds of grain diameters, at a point in a permeable medium that is free of boundary effects. Megascopic dispersion is the one-dimensional (1D) dispersion derived by averaging across an entire cross section. This work investigates how both dispersions vary with heterogeneity, aspect ratio, diffusion coefficient, and autocorrelation. The theoretical results are compared to existing field and laboratory data and to existing theories for limiting cases. The degree of autocorrelation in the medium determines whether or not megascopic dispersivity (dispersion coefficient divided by velocity) is uniquely defined. Large correlation distances (with respect to the medium dimensions) imply a dispersivity that grows with distance traveled. Small correlation distances imply a dispersivity that is eventually stabilized at some constant value. This value is related to the heterogeneity of the medium. On the field scale, diffusion is insignificant, but on a laboratory scale, it can stabilize the dispersivity even if the medium is correlated. Macroscopic dispersivity is sensitive to diffusion in both the laboratory and field scale. It is smaller than or equal to megascopic dispersivity, also in conformance with experimental data, and comparable to laboratory-measured dispersivity. Introduction Dispersion is mixing caused by variations (heterogeneity) in the velocity within each flow channel and from one channel to another. Molecular diffusion is the transport of mass because of spatial con-centration differences. Dispersion and diffusion in permeable media play an important role in miscible displacement, where channeling play an important role in miscible displacement, where channeling and/or fingering of the displacing fluid occurs. We examine the interrelationship between heterogeneity and diffusion in this paper. Purpose and Scope Purpose and Scope In this paper. mixing resulting from macroscopic variations in the permeability of the medium is of primary interest. These permeability of the medium is of primary interest. These heterogeneities cause fluctuations in the velocities of individual fluid ele-ments. To focus on the mixing resulting from heterogeneity and diffusion, the process under consideration is one in which one fluid displaces another fully miscible fluid. The investigative tool is nu-merical simulation of first-contact-miscible, equal-density, constant mobility displacements in two-dimensional (2D), randomly heterogeneous (RH) flow fields. A primary purpose of this work is to investigate the behavior of longitudinal dispersivity in field-scale miscible displacements. We place special emphasis on analyzing systems with large heterogeneity (Dykstra-Parsons coefficient, VDP = 0.6 to 0.8), which is the norm in oilfield cores. These values are considerably higher than those generally investigated in the past. We also investigate the effects of diffusion and system aspect ratios [system length parallel to bulk flow divided by length perpendicular to flow (L/b)] parallel to bulk flow divided by length perpendicular to flow (L/b)] on the behavior of longitudinal dispersivity. Definitions Macroscopic dispersion is the mixing, on the scale of several hundreds of grain diameters, at a point in a permeable medium that is free of boundary effects. Megascopic dispersion is the 1D dispersion derived by averaging across an entire cross section. The megascopic description is typically the size of a gridblock in a numerical reservoir simulation model and contains many macroscopic elements. The megascopic dispersivity, alpha ME, is important in field-scale simulation of EOR processes because it controls volumetric sweep efficiency within a gridblock. A macroscopic description describes a permeable medium in terms of average properties and their variations at scales much larger than pores. In EOR, the macroscopic dispersivity, alpha MA, controls oil pores. In EOR, the macroscopic dispersivity, alpha MA, controls oil recovery by determining the rate of formation of an effective oil-recovering mixture in the pores. This happens in developed miscibl floods or through the generation of an optimal salinity in micellar/ polymer floods. polymer floods. Megascopic and macroscopic do not necessarily coincide with field and laboratory scales. The dispersivity measured in a laboratory experiment is megascopic, but it differs from a field-scale megascopic dispersivity because of a smaller heterogeneity, a generally smaller aspect ratio, and a greater influence of lateral boundaries. We shall see below that megascopic dispersivities measured on laboratory displacements are comparable to the macroscopic dispersivity in a field-scale displacement. Both macroscopic and megascopic dispersions in a permeable medium result from contrasts in hydraulic conductivity. Generally, the larger the contrast between the elements that make up the medium, the larger the dispersion. In these cases, mixing is produced by permeable-medium nonidealities that are responsible for changes in the direction and velocity of flow. For most geologic systems of interest, the most significant dispersion will be generated by this mechanism.