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Horizontal wells are a very important element in oil and gas industry due to their distinguished advantages. Horizontal wells are not technically horizontal. This is because of the structural nature of reservoir formations and drilling procedures. In response to the reservoir rock’s strength, the horizontal well deviates upward and downward while being drilled forming an undulating path instead of a horizontal. In this study, horizontal wells with an undulating trajectory within a gas reservoir have been studied. The aim of this research is to investigate the effect of the trajectory angle on pressure drop in horizontal wells. In addition, the contribution of water flow to pressure drop is a part of this research. Generally, water comes from different sources like an aquifer or a water flood job. In low permeability horizontal wells, hydraulic fracturing introduces water to gas wells. Water distribution is an important issue in gas wells production. In order to achieve the goal of this study, a model has been developed to simulate different situations for a horizontal well with an undulating trajectory in gas reservoirs. This study is a step forward to understand well performance in low permeability gas reservoirs.

This paper is now in two parts. In the first part a new exact solution of the plane flight of a particle is discussed, by which it is possible to take a very long first arc straight from tables of functions defined in the solution. Fairly extensive tables of these functions have been computed (42 sets of each function:- a total of 1,900 entries). Having devised a method of computation, the writer employed another to do this work, and accordingly omits them from this edition, every part of which, to the best of his belief, is original and unaided. A series solution for the lower arcs is also discussed in Part I. In Part II, solutions in finite terms of the vertical fall of a particle, an approximate solution of the plane flight, and of the effect of changing winds are given.

Compact facility designs and retro-fitting of facilities that involve heavy lifts are often performed in congested areas. Tight schedules increase the requirement to provide detailed heavy lift analysis. The planning of every aspect of a critical lift operation is essential. Managing the behavior and trajectory of the lifted object during the lift is often left to the field crew. The rigger signalman and the crane operator communicate by radio, or by hand signals, to maneuver the lifted object between obstructions. This thesis presents advancements in the development of mathematical algorithms for the lift object trajectory path and analysis. The proposed methodology is divided into smaller manageable phases to control the process and at the same time create independent modules. Each step of the lifted object movement was algebraically-digitally tracked, starting at the lifted object pick-point through an optimum path development to the objects final position or set-point. Parameters such as the minimum distance between the lifted object and passing obstructions and the minimum clearance between the lifted object and the crane boom envelope are some of the many predefined rules that were taken into account. Each step in the developed algorithm provides a short description, partial decision flowchart, and graphical interpretation of the problem, and some sections cover mathematical calculations of a defined path. The lifted objects spatial trajectory analysis and optimization are part of the complex assignment relating to the crane selection process. The proposed methodology is tested on a case study, which is also described in this thesis in order to illustrate the essential features of the proposed methodology. / Construction Engineering and Management

Thesis (M.S. in Astronautical Engineering)--Naval Postgraduate School, Sept. 2004. / Thesis Advisor(s): I. Michael. Ross. Includes bibliographical references (p. 127-129). Also available online.

Thesis (M.S. in Applied Mathematics)--Naval Postgraduate School, June 2010. / Thesis Advisor(s): Kang, Wei ; Second Reader: Zhou, Hong. "June 2010." Description based on title screen as viewed on July 14, 2010. Author(s) subject terms: Nonlinear model, trajectory optimization, state and control variables, cost function Includes bibliographical references (p. 59-60). Also available in print.

Advanced connected and automated vehicle technologies offer new opportunities for highway traffic smoothing by optimizing automated vehicle trajectories. As one of the pioneering attempts, this study proposes an efficient trajectory optimization algorithm that can simultaneously improve a range of performance measures for a platoon of vehicles on a signalized highway section. This optimization is centered at a novel shooting heuristic (SH) for trajectory construction that considers realistic constraints including vehicle kinematic limits, traffic arrival patterns, carollowing safety, and signal operations. SH has a very parsimonious structure (e.g., only four acceleration parameters) and a very small computational complexity. Therefore, it is suitable for real-time applications when relevant technologies are in place in the near future. This study lays a solid foundation for devising holistic cooperative control strategies on a general transportation network with emerging technologies.

Analysis of measured data is often required when there is no deep understanding of the mathematics that accurately describes the process being measured. Additionally, realistic estimation of the derivative of measured data is often useful. Current techniques of accomplishing this type of data analysis are labor intensive, prone to significant error, and highly dependent on the expertise of the engineer performing the analysis. The ?Self-Smoothing Functional Estimation? (SSFE) algorithm was developed to automate the analysis of measured data and to provide a reliable basis for the extraction of derivative information. In addition to the mathematical development of the SSFE algorithm, an example is included in Chapter III that illustrates several of the innovative features of the SSFE and associated algorithms. Conclusions are drawn about the usefulness of the algorithm from an engineering perspective and additional possible uses are mentioned.

The proliferation of mobile devices and advances in geo-positioning technologies has fueled the growth of location-based applications, systems and services. Many location-based applications have now gained high popularity and permeated the daily activities of mobile users. This has led to a huge amount of geo-location data generated on a daily basis, which draws significant interests in analyzing and mining ubiquitous location data, especially trajectories of mobile objects moving in road networks (MO trajectories). Mobile trajectories are complex spatio-temporal sequences of location points with varying sample sizes and varying lengths. Mining interesting patterns from large collection of complex MO trajectories presents interesting challenges and opportunities which can reveal valuable insights to the studies of human mobility in many perspectives. This dissertation research contributes original ideas and innovative techniques for mining complex trajectories from whole trajectories, from subtrajectories of significant characteristics, and from semantic location sequences within large-scale datasets of MO trajectories. Concretely, the first unique contribution of this dissertation is the development of NEAT, a three-phase road-network aware trajectory clustering framework to organize MO subtrajectories into spatial clusters representing highly dense and highly continuous traffic flows in a road network. Compared with existing trajectory clustering approaches, NEAT yields highly accurate clustering results and runs orders of magnitude faster by smartly utilizing traffic locality with respect to physical constraints of the road network, traffic flows among consecutive road segments and flow-based density of mobile traffic as well as road network based distances. The second original contribution of this dissertation is the design and development of TraceMob, a methodical and high performance framework for clustering whole trajectories of mobile objects. To our best knowledge, this is the first whole trajectory clustering system for MO trajectories in road networks. The core idea of TraceMob is to develop a road-network aware transformation algorithm that can map complex trajectories of varying lengths from a road network space into a multidimensional data space while preserving the relative distances between complex trajectories in the transformed metric space. The third novel contribution is the design and implementation of a fast and effective trajectory pattern mining algorithm TrajPod. TrajPod can extract the complete set of frequent trajectory patterns from large-scale trajectory datasets by utilizing space-efficient data structures and locality-aware spatial and temporal correlations for computational efficiency. A comprehensive performance study shows that TrajPod outperforms existing sequential pattern mining algorithms by an order of magnitude.