Application of stability theory and finite element simulation to characterize miscible displacements.

摘要

Hydrodynamic instability, which results in viscous fingering, is a major factor that limits the success of miscible displacement projects in the field. The ability to predict its occurrence would contribute significantly towards the design of stable and efficient miscible projects for enhanced oil recovery.;In this study, a new stability theory was developed to predict the onset of instability during miscible displacement in petroleum reservoirs. Specifically, a universal dimensionless number and its critical value for the onset of instability, were derived. Knowing the pertinent parameters of a proposed miscible project such as viscosity ratio, the density difference, the effective dispersion coefficients, the macroscopic dimensions of the porous medium, and the injection rate, the stability number can be used to predict whether the displacement will be stable or unstable.;With a two-dimensional Galerkin-based Finite Element simulator, systematic numerical studies were conducted to investigate the subsequent behavior of the displacements in homogeneous and heterogeneous porous media for favorable and unfavorable mobility ratios over a wide range of the new dimension less stability number. The results indicate that a favorable mobility ratio displacement is unconditionally stable whereas an unfavorable mobility ratio displacement is conditionally stable. The effect of heterogeneity is to induce some form of macroscopic dispersion which dampens but does not entirely eliminate instabilities, suggesting that displacement in-situ will be unstable if the necessary and sufficient conditions for instability are met.;Further, the results of numerical simulations and reported laboratory experiments using liquid-liquid fluids show good agreement with theory. These results have shed considerable light on the factors that control the phenomenon of instability. Such information can be useful in the optimal design of miscible projects aimed at the minimization of the adverse impact of instability and the achievement of good oil recovery. A consequence of this theory is a model proposed to calculate the optimum size requirements for a solvent slug displacement process.