## Abstract

We discuss the notion of the well productivity index (PI) for the generalized Forchheimer ow of uid through porous media. The PI characterizes the well capacity with respect to drainage area of the well and in general is time dependent. In case of the slightly compressible uid the PI stabilizes in time to the specific value, determined by the so-called pseudo steady state solution, [5, 3, 4]. Here we generalize our results from [4] in case of arbitrary order of the nonlinearity of the ow. In case of the compressible gas ow the mathematical model of the PI is studied for the first time. In contrast to slightly compressible uid the PI stays "almost" constant for a long period of time, but then it blows up as time approaches the certain critical value. This value depends on the initial data (initial reserves) of the reservoir. The "greater" are the initial reserves, the larger is this critical value. We present numerical and theoretical results for the time asymptotic of the PI and its stability with respect to the initial data.

Original language | English |
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Journal | Evolution Equations and Control Theory |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 2016 |

## Keywords

- Compressible fluid
- Forchheimer flow
- Gas flow
- Nonlinear flow
- Pro-ductivity index