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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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…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…