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

…outlet.
For the time-independent well production rate (total flux across the well outlet), the corresponding flow regime is called ”*Pseudo*-*Steady* *State*” (PSS) regime,
if the corresponding pressure drawdown is constant. We observe that…

…the
*pseudo* *steady* *state* solution for this problem. Also we define the well productivity
index and analyze the productivity index for the *pseudo* *steady* *state* case.
2.1.1 Time-dependent analysis
Darcy’s law is commonly related to monophasic viscous fluid…

…Γw
2.1.2 Time-Independent Analysis (*Pseudo* *Steady* *State* Solution)
Definition 2.1.1. Let the well production rate Q be time independent:
u(x, t) · ndsx = Q.
Γw
We will call the flow regime a ”*Pseudo*-*Steady* *State*” (PSS)…

…x28;∇w) + kγ(∇w)2 }.
(2.48)
Since (2.48) depends on t, we cannot obtain a *Pseudo* *Steady* *State* solution for this
case.
2.3 PSS Analysis with φ as a function of x
Conversely to the previous sections, in this…

…section we assume the porosity of
the porous media, φ(x) to be space dependent. With this assumption, we derive the
*pseudo* *steady* *state* solution for this case. Furthermore we derive expressions for the
well productivity index.
After neglecting…

…the second system, the permeability of the top layer is exactly equal to 0. For the
*Pseudo* *Steady* *State* regime, the Productivity index of the former case must converge
to the latter case.
With its original definition the convergence of the Productivity…

…*steady* *state* boundary
value problem,
−γAφ = ∇ · (k∇w) + kγ(∇w)2 ,
(2.16)
w(x) |Γw = 0 ,
∂w
∂n
= 0.
(2.17)
(2.18)
Γe
Proposition 2.1.2. (1) Let w(x) be the solution of…

…x28;x, 0) = P0 .
(2.52)
with initial condition
12
Texas Tech University, P.A. Janitha Gunatilake, December 2010
Let w(x) be a solution to the auxiliary *steady* *state* boundary value problem
−γφ(x)A = ∇ · (k∇w…