## Abstract

The steady axisymmetric flow of an incompressible fluid into a vertical well hydrodynamically perfectly drilled into a stratified inhomogeneous half-space consisting of three layers with different permeabilities is considered. The boundaries of the layers are assumed to be horizontal planes and the roof of the upper layer is assumed to be impermeable. The flow obeys a linear Darcy's law. The pressure distribution on the well is assumed to be given, which is the main obstacle to finding an exact solution of the problem. Beginning with the classical studies of Muskat and Charnyi [1, 2], approximate solutions of such problems have been constructed as a superposition of flows generated by point sources with given intensities, distributed along the well axis in accordance with a fairly simple law. In the present study, this approach is used to obtain an integral equation for the source density distribution, which is then solved numerically. Comparison with the known exact solution for a thin elongated ellipsoid ("needle") shows that this approach makes it possible to ensure an accuracy which at any rate is sufficient for applications.

Original language | English |
---|---|

Pages (from-to) | 71-78 |

Number of pages | 8 |

Journal | Fluid Dynamics |

Volume | 42 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2007 |

Externally published | Yes |

## Keywords

- Axisymmetric flow into a well
- Stratified inhomogeneous bed