Linear Stability of Miscible Displacement Processes in Porous Media in the Absence of Dispersion

1986 ◽  
Vol 74 (2) ◽  
pp. 93-115 ◽  
Author(s):  
F. J. Hickernell ◽  
Y. C. Yortsos
Keyword(s):  
Porous Media ◽  
Linear Stability ◽  
Miscible Displacement ◽  
Displacement Processes

A New Method To Simulate the Effects of Viscous Fingering on Miscible Displacement Processes in Porous Media

1984 ◽  
Vol 24 (01) ◽  
pp. 56-64 ◽  
Author(s):  
Shapour Vossoughi ◽  
James E. Smith ◽  
Don W. Green ◽  
G. Paul Willhite
Keyword(s):  
Porous Media ◽  
Dispersion Equation ◽  
Viscosity Ratio ◽  
Laboratory Data ◽  
Viscous Fingering ◽  
Miscible Displacement ◽  
Concentration Profiles ◽  
Flow Function ◽  
Fractional Flow ◽  
Displacement Processes

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.

Fingering instabilities in vertical miscible displacement flows in porous media

1995 ◽  
Vol 288 ◽  
pp. 75-102 ◽  
Author(s):  
O. Manickam ◽  
G. M. Homsy
Keyword(s):  
Porous Media ◽  
Stability Analysis ◽  
Linear Stability ◽  
Critical Velocity ◽  
Linear Stability Analysis ◽  
Miscible Displacement ◽  
Stable Region ◽  
Miscible Displacements ◽  
Flows In Porous Media ◽  
Two Fluids

The fingering instabilities in vertical miscible displacement flows in porous media driven by both viscosity and density contrasts are studied using linear stability analysis and direct numerical simulations. The conditions under which vertical flows are different from horizontal flows are derived. A linear stability analysis of a sharp interface gives an expression for the critical velocity that determines the stability of the flow. It is shown that the critical velocity does not remain constant but changes as the two fluids disperse into each other. In a diffused profile, the flow can develop a potentially stable region followed downstream by a potentially unstable region or vice versa depending on the flow velocity, viscosity and density profiles, leading to the potential for ‘reverse’ fingering. As the flow evolves into the nonlinear regime, the strength and location of the stable region changes, which adds to the complexity and richness of finger propagation. The flow is numerically simulated using a Hartley-transform-based spectral method to study the nonlinear evolution of the instabilities. The simulations are validated by comparing to experiments. Miscible displacements with linear density and exponential viscosity dependencies on concentration are simulated to study the effects of stable zones on finger propagation. The growth rates of the mixing zone are parametrically obtained for various injection velocities and viscosity ratios.

Sign in / Sign up

Export Citation Format

Share Document