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

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…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…