Full Record

Author | Gunatilake, Janitha |

Title | Modeling and simulation for the evaluation of the productivity index in stratified reservoir-well systems |

URL | http://hdl.handle.net/2346/ETD-TTU-2010-12-1128 |

Publication Date | 2010 |

Date Accessioned | 2016-11-14 23:11:30 |

Discipline/Department | Mathematics and Statistics |

University/Publisher | Texas Tech University |

Abstract | Our research is mainly focused on modeling the "Productivity Index" of a two-layered reservoir well system with linear Darcy flow. In particular, we consider two systems. For the first system, the permeability of the top layer is relatively small and is approaching to 0. The permeability of the top layer is exactly equal to 0 in the second system. For the Pseudo Steady State regime, we want the Productivity index of the former case to be convergent to the latter case. From the governing equations of the fluid flow in porous media, we develop a theoretical model for the system. Since we do not get the required convergence with the existing definition of the Productivity Index, we introduce a new definition to the Productivity Index taking porosity of the porous media into account. With this new definition, it was conjectured that under certain restrictions to the porosity, the first system converges to the second system. This conjecture was validated by the simulation results. |

Subjects/Keywords | Porous media; Productivity index; Multi-layer reservoir; Pseudo steady state |

Contributors | Aulisa, Eugenio (Committee Chair); Ibragimov, Akif (committee member); Toda, Magdalena D. (committee member) |

Language | en |

Rights | Unrestricted. |

Country of Publication | us |

Record ID | handle:2346/ETD-TTU-2010-12-1128 |

Repository | tdl |

Date Indexed | 2020-04-11 |

Sample Search Hits | Sample Images

…Furthermore
it is assumed that each *layer* is homogeneous with constant permeability and the well
has constant conductivity. Γw is the well-outlet and U = U1 + U2 + U3 is the domain
of the *reservoir*-well system.
Figure 1.1: 2D scheme of the fully penetrated…

…for PSS the
corresponding PI is also constant.
In our research, we consider two well-*reservoir* systems: in the first the permeability of the top *layer* k1 approaches to 0, in the second k1 is exactly equal to 0. The
1
Texas Tech University, P.A…

…Janitha Gunatilake, December 2010
latter corresponds to the *reservoir*-well system where the top *layer* has been removed.
See Figure 1.2.
(a) k1 = 0, k1 → 0
(b) k1 = 0
Figure 1.2: The 2 cases considered in our research.
From a…

…been
reached.
Let k1 , k2 and k3 be constants. We assume k = k1 for the top *layer* of the
*reservoir*, U 1 and k = k2 for the bottom *layer* of the *reservoir*. Furthermore, we
assume k = k3 for the well.
The geometrical parameters are:
x1 = 0.5,
x2 = 100,
y1…

…of the top *layer*, k1
approaching to 0 and k1 exactly equal to 0, which is similar to top *layer* removed
from the *reservoir*. See Figure 3.2. As k1 approaches 0, the former system should
(a) k1 = 0, k1 → 0
(b) k1 = 0
Figure 3.2…

…Texas Tech University, P.A. Janitha Gunatilake, December 2010
CHAPTER IV
CONCLUSIONS
For the two-layered *reservoir*-well system, two systems were considered. For the
first system, the permeability of the top *layer* is relatively small and approaches 0.
In…

…Texas Tech University, P.A. Janitha Gunatilake, December 2010
CHAPTER I
INTRODUCTION
We consider a two-layered *reservoir* well system, with a fully penetrated vertical
well located at the left side of the geometry, as depicted in Figure 1.1…

…vertical well in the two-layered rectangular *reservoir*.
The Productivity Index (PI) is a characteristic of the *reservoir*-well system and
is a measure of its ability to produce oil from the well outlet. From the definition
used in petroleum…