Dispersion is the irreversible mixing that occurs during miscible displacements. Dispersion can reduce local displacement efficiency by lessening solvent peak concentration or increase volumetric sweep efficiency by spreading of the injected solvent to more of the reservoir. Dispersion is therefore an important parameter in predicting and simulating miscible displacements. The difficulty of simulating miscible displacement and understanding the effect of dispersion is also compounded by numerical dispersion, which increases the apparent dispersion in finite-difference simulation models. This paper presents an approach to estimate the total longitudinal and transverse dispersion in large-scale media by use of continuous solvent injection in a medium of finite thickness. The simulations are based on the experimental arrangement of Blackwell (1962) to estimate transverse dispersion, with experiments consisting of coinjecting two miscible fluids into different sections of the medium at similar rates. This model arrangement, coupled with analytical solutions for the 2D convection/dispersion equation for a continuously injected solvent, allows us to determine longitudinal and transverse dispersivity simultaneously for the flow medium. In this manner, we investigate the effects of stochastic permeability distributions and other scaling groups affecting first-contact-miscible simulations on dispersion. Sensitivity analysis of dispersion in stochastic permeability fields confirms that both longitudinal and transverse dispersion are scale dependent. Results also show that the effect of increasing autocorrelation of cell permeability in the longitudinal direction (parallel to flow) is to increase longitudinal dispersion, as solvent travels through more continuous layers, while reducing transverse dispersion. Increasing autocorrelation in the transverse direction reduces dispersion in both directions. This reduction is caused by equilibration of solvent concentrations in continuous sections of the reservoir, resulting in reduced solute fingering and channeling. Finally, we developed a simple procedure to use the estimated dispersivities to determine a priori the maximum gridblock size that will maintain an equivalent level of dispersion between finescale models and upscaled coarse models. Large gridblock sizes can be used for highly heterogeneous and layered reservoir models. Nonuniform coarsening (upscaling) methods were also recommended and validated for reservoir models with sets of sequential but different permeability distributions. The procedure was extended to multicontact miscible simulations. The sweep and recovery from upscaled multicontact miscible simulations were comparable with those of fine-scale models.
All Science Journal Classification (ASJC) codes
- Energy Engineering and Power Technology
- Geotechnical Engineering and Engineering Geology