Abstract
Dispersion and viscous fingering are important parameters in miscible displacement. Effects of dispersion on concentration profiles in porous media can be simulated when the viscosity ratio is favorable. The capability to simulate viscous fingering is limited.
This paper presents a new method to simulate effects of viscous fingering on miscible displacement processes in porous media. The method is based on the numerical solution of a general form of the convection-dispersion equation. In this equation the convection term is represented by a fractional flow function. The fractional flow function is derived from Darcy's law by using a concentration-dependent average viscosity and relative flow area to each fluid at any point in the bed.
The method was extended to the description of a polymer flood by including retention and inaccessible PV. A Langmuir-type model for polymer retention in the rock was used. The resulting convection-dispersion equation for displacement by polymer was solved numerically by the use of a finite-element method with linear basis functions and Crank-Nicholson derivative approximation.
History matches were performed on four sets of laboratory data to verify the model:an unfavorable viscosity ratio displacement,stable displacement of glycerol by polymer solution,unstable displacement of brine by a slug of polymer solution, anda favorable viscosity ratio displacement.
In general, computed results from the model matched laboratory data closely. Good agreement of the model with experiments over a significant range of variables lends support to the analysis.
Introduction
Considerable effort has been directed to the study of dispersion phenomena in flow through porous media. Dispersion phenomena become important in EOR techniques, especially those involving the use of chemical slugs such as a micellar/polymer flood. Because the micellar solution is expensive, a carefully designed polymer buffer solution must be injected between the microemulsion and the drive water. This minimizes the effect of mixing and dispersion that otherwise would cause the micellar slug to lose its effectiveness.
Aronofsky and Heller1 were among the first to use the diffusion or dispersion model to describe miscible displacement. This employs Fick's law of diffusion to describe the transport of mass within the zone containing both displacing and displaced fluids. The so-called convection-dispersion equation obtained by differential material balance has become generally accepted as the basis for analysis of miscible displacements. The dispersion equation has been solved numerically2–6 as well as analytically6,7 to obtain concentration profiles and dispersion coefficients. However, the prediction fails whenever viscous fingering occurs.
Viscous fingering is the result of an unstable displacement of a more viscous fluid by a less viscous fluid. Finger-shaped intrusions of the displacing fluid into the displaced fluid have been observed and reported in the literature8–11 for miscible as well as immiscible displacements.
A virtual element method for the miscible displacement of incompressible fluids in porous media
