Browsing by Subject "Productivity index"
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Item Mathematical model for darcy forchheimer flow with applications to well performance analysis(2007-08) Amao, Abiodun Matthew; Siddiqui, Shameem; Ibragimov, Akif; Aulisa, Eugenio; Heinze, Lloyd R.Well performance and productivity evaluation is a fundamental role of petroleum engineers and this is done at different phases of petroleum production; from the reservoir to the well bore through the tubulars and ultimately to the stock tank. This task requires physical and mathematical models that adequately characterizes oil and gas flow at these different phases of petroleum production. This thesis reviews different scenarios where the effects of non-linearity in flow is apparent in petroleum and gas reservoirs and can not be neglected any more. Laboratory experiments were carried out on core samples to show non-linearity in flow, which confirms deviation from the traditional Darcy law, used in reservoir flow modeling. Historically non-Darcy flow has only been reckoned with in high flow rate gas wells, in which it has been treated as a 'rate dependent' skin factor and has been assumed to act only in the vicinity of the well-bore, while neglecting the reservoir. This work seeks to show the inherent errors due to the negligence of this phenomenon, which is fundamental to the calculation of the productivity index of the well. Using the modified non-linear Darcy law as the equation of motion to model filtration in porous media, this new model is compared to the conventional Darcy law. Proposed method delivers robust framework to model non-linear flow in the reservoir. The result of this project will contribute to knowledge by equipping reservoir engineers with a robust technique to analyze well performance; this approach will provide better evaluation tool for selecting wells for remedial operations such as work-over or stimulation.Item Modeling and simulation for the evaluation of the productivity index in stratified reservoir-well systems(2010-12) Gunatilake, Janitha; Aulisa, Eugenio; Ibragimov, Akif; Toda, Magdalena D.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.Item Revised productivity index equation to improve transient history match for the Capacitance Resistance Model(2016-12) Pan, Zhong; Lake, Larry W.The Capacitance Resistance Model (CRM) is a data-driven reservoir model developed for well surveillance and management. The model is gaining popularity in reservoir engineering community because of its simplicity and ability to provide insights on well-to-well connectivity during water/gas flooding project. Furthermore, the model can be used to optimize injection scheme or even plan for infill drilling. The model was built on the assumptions that during waterflooding the dominant flow regime is semi-steady state. However, to extend the functionality of this model to unconventional reservoirs, a productivity index model that works well in transient flow regime should be investigated. In this thesis, two different productivity models are proposed. The first is the combined productivity index model. This model originates from the analytical solution of single compartment model and the constant behavior of the productivity index in fracture-dominated flow. These two components are then linearly combined to form a new productivity index model. The second is the logistic productivity index model, which uses a well-studied logistic growth model to capture the S-shaped production profile starting from a transient linear flow regime to a late-time fracture-dominated regime. These two proposed productivity index models are incorporated into the fundamental CRM equation, respectively, to derive the logistic CRM and combined CRM. To validate the models, multiple reservoir simulations were conducted to generate synthetic cases capturing both transient linear flow and fracture-dominated regime, and then the proposed models were fitted to the simulation data using Microsoft Excel Solver. Case validation is also accomplished with field data. Very good history matches were obtained from these two models, and they demonstrate that with proper revision to semi-steady state model CRM is able to match production history sufficiently and quickly. In addition, the combined CRM is physics-based so it is shown that the model is able to provide insights on some important reservoir properties.