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Physics of Fluids / Volume 30 / Issue 10

Phys. Fluids 30, 2928 (1987); http://dx.doi.org/10.1063/1.866070 (8 pages)

Stability of displacement processes in porous media in radial flow geometries

Y. C. Yortsos

Departments of Petroleum and Chemical Engineering, University of Southern California, Los Angeles, California 90089‐1211

(Received 12 March 1987; accepted 2 June 1987)

The linear stability of certain displacement processes in porous media for two‐dimensional radial flows induced by a point source is examined. Both two‐phase, immiscible displacement and single‐phase miscible displacement in the presence of equilibrium adsorption are discussed. In agreement with Tan and Homsy [Phys. Fluids 30, 1239 (1987)], it is found that disturbances grow or decay algebraically in time. Via appropriate transformations the eigenvalue problems are shown to be identical to those in rectilinear flow geometries with suitably modified base states and parameters. Thus several stability features are inferred directly from the analysis in rectilinear geometries. The results indicate the existence of critical values for the capillary (NCa) or Peclet (Pe) number, above which the displacement is unstable for wavenumbers in a band of finite width. For large NCa or Pe the most dangerous and the highest cutoff modes scale linearly with NCa or Pe. The different scaling found by Tan and Homsy [Phys. Fluids 30, 1239 (1987)] follows directly as a singular limit of the miscible displacement problem in the absence of adsorption.

KEYWORDS and PACS

Keywords

POROUS MATERIALS, STABILITY, DISPLACEMENTS, LAMINAR FLOW, POINT SOURCES, TWO−PHASE FLOW, MISCIBLE−PHASE DISPLACEMENT, IMMISCIBILITY, ADSORPTION, DISTURBANCES, EIGENVALUES, TRANSFORMATIONS, EQUILIBRIUM

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.866070

PUBLICATION DATA

ISSN

0031-9171 (print)  

For access to fully linked references, you need to log in.
    C. T. Tan and G. M. Homsy, Phys. Fluids 30, 1239 (1987PFLDAS000030000005001239000001).

    C. T. Tan and G. M. Homsy, Phys. Fluids 29, 3549 (1986PFLDAS000029000011003549000001).


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