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**Stability of miscible displacements in porous media: rectilinear flow.**
*(English)*
Zbl 0608.76087

A theoretical treatment of the stability of miscible displacement in a porous medium is presented. For a rectilinear displacement process, since the base state of uniform velocity and a dispersive concentration profile is time dependent, we make the quasi-steady-state approximation that the base state evolves slowly with respect to the growth of disturbances, leading to predictions of the growth rate.

Comparison of results with initial value solutions of the partial differential equations shows that, excluding short times, there is good agreement between the two theories. Comparison of the theory with several experiments in the literature indicates that the theory gives a good prediction of the most dangerous wavelength of unstable fingers. An approximate analysis for transversely anisotropic media has elucidated the role of transverse dispersion in controlling the length scale of fingers.

Comparison of results with initial value solutions of the partial differential equations shows that, excluding short times, there is good agreement between the two theories. Comparison of the theory with several experiments in the literature indicates that the theory gives a good prediction of the most dangerous wavelength of unstable fingers. An approximate analysis for transversely anisotropic media has elucidated the role of transverse dispersion in controlling the length scale of fingers.

### MSC:

76S05 | Flows in porous media; filtration; seepage |

76E99 | Hydrodynamic stability |

76T99 | Multiphase and multicomponent flows |

76M99 | Basic methods in fluid mechanics |

### Keywords:

stability; miscible displacement; porous medium; rectilinear displacement process; dispersive concentration profile; quasi-steady-state approximation; initial value solutions; approximate analysis; transversely anisotropic media; length scale of fingers
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\textit{C. T. Tan} and \textit{G. M. Homsy}, Phys. Fluids 29, 3549--3556 (1986; Zbl 0608.76087)

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### References:

[1] | Hill, Chem. Eng. Sci. 1 pp 247– (1952) |

[2] | Chouke, Trans. AIME 213 pp 103– (1958) |

[3] | Perrine, Soc. Pet. Eng. J. 1 pp 17– (1961) |

[4] | Heller, J. Appl. Phys. 37 pp 1566– (1966) |

[5] | Schowalter, AIChE J. 11 pp 99– (1965) |

[6] | Wooding, Z. Angew. Math. Phys. 13 pp 255– (1962) |

[7] | R. L. Chouke, inProceedings of the Society of Petroleum EngineersDepartment of Energy Third Joint Symposium on Enhanced Oil Recovery, Tulsa, Oklahoma, 1982, SPE-10686, Appendix of J. W. Gardner and J. G. J. Ypma (Soc. Pet. Eng., Dallas, TX, 1982). |

[8] | Davis, Ann. Rev. Fluid Mech. 8 pp 57– (1976) |

[9] | Perkins, Soc. Pet. Eng. J. 3 pp 70– (1963) |

[10] | Slobod, Soc. Pet. Eng. J. 3 pp 9– (1963) |

[11] | Perkins, Soc. Pet. Eng. J. 5 pp 301– (1965) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.