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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.

Solutions to trajectory optimization problems are carried out by the direct and indirect methods. Under broad heading of these methods, numerous algorithms such as collocation, direct, indirect and multiple shooting methods have been developed and reported in the literature. Each of these algorithms has certain advantages and limitations. For example, direct shooting technique is not suitable when the number of nonlinear programming variables is large. Indirect shooting method requires analytical derivatives of the control and co-states function and a poorly guessed initial condition can result in numerical unstable values of the adjoint variable. Multiple shooting techniques can alleviate some of these difficulties by breaking down the trajectory into several segments that help in reducing the non-linearity effects of early control on later parts of the trajectory. However, multiple shooting methods then have to handle more number of variables and constraints to satisfy the defects at the segment joints. The sie of the nonlinear programming problem in the collocation method is also large and proper locations of grid points are necessary to satisfy all the path constraints. Stochastic methods such as Genetic algorithms, on the other hand, also require large number of function evaluations before convergence. To overcome some of the limitations of the conventional methods, improved solution techniques are developed. Three improved methods are proposed for the solution of trajectory optimization problems. They are • a genetic algorithm employing dominance and diploidy concept. • a collocation method using chebyshev polynomials , and • a hybrid method that combines collocation and direct shooting technique A conventional binary-coded genetic algorithm uses a haploid chromosome, where a single string contains all the variable information in the coded from. A diploid, as the name suggests, uses pair of chromosomes to store the same characteristic feature. The diploid genetic algorithm uses a dominant map for decoding genotype into a stable, consistent phenotype. In dominance, one allele takes precedence over another. Diploidy and dominance helps in retaining the previous best solution discovered and shields them from harmful selection in a changing environment. Hence, diploid and dominance affect a king of long-term memory in the genetic algorithm. They allow alternate solutions to co-exist. One solution is expressed and the other is held in abeyance. In the improved diploid genetic algorithm, dominant and recessive genes are defined based on the fitness evaluation of each string. The genotype of fittest string is declared as the dominant map. The dominant map is dynamic in nature as it is replaced with a better individual in future generations. The concept of diploidy and dominance in the improved method mimics closer to the principles used in human genetics as compared to any such algorithms reported in the literature. It is observed that the improved diploid genetic algorithm is able to locate the optima for a given trajectory optimization problem with 10% lower computational time as compared to the haploid genetic algorithm. A parameter optimization problem arising from an optimal control problem where states and control are approximated by piecewise Chebyshev polynomials is well known. These polynomials are more accurate than the interpolating segments involving equal spaced data. In the collocation method involving Chebyshev polynomials, derivatives of two neighboring polynomials are matched with the dynamics at the nodal points. This leads to a large number of equality constraints in the optimization problem. In the improved method, derivative of the polynomial is also matched with the dynamics at the center of segments. Though is appears the problem size is merely increased, the additional computations improve the accuracy of the polynomial for a larger segment. The implicit integration step size is enhanced and overall size of the problem is brought down to one-fourth of the problem size defined with a conventional collocation method using Chebyshev polynomials. Hybrid method uses both collocation and direct shooting techniques. Advantages of both the methods are combined to give more synergy. Collocation method is used in the starting phase of the hybrid method. The disadvantage of standalone collocation method is that tuning of grid points is required to satisfy the path constraints. Nevertheless, collocation method does give a good guess required for the terminal phase of the hybrid method, which uses a direct shooting approach. Results show nearly 30% reduction in computation time for the hybrid approach as compared to a method in which direct shooting alone is used, for the same initial guess of control. The solutions obtained from the three improved methods are compared with an indirect method. The indirect method requires derivations of the control and adjoint equations, which are difficult and problem specific. Due to sensitivity of the costate variables, it is often difficult to find a solution through the indirect method. Nevertheless, these methods do provide an accurate result, which defines a benchmark for comparing the solutions obtained through the improved methods. Trajectory design and optimization of a RLV(Reusable Launch Vehicle) Demonstrator mission is considered as a test problem for evaluating the performance of the improved methods. The optimization problem is difficult than a conventional launch vehicle trajectory optimization problem because of the following two reasons. • aerodynamic lift forces in the RLV add one more dimension to the already complex launch vehicle optimization problem. • as RLV performs a sub orbital flight, the ascent phase trajectory influences the re-entry trajectory. Both the ascent and re-entry optimization problem of the RLV mission is addressed. It is observed that the hybrid method gives accurate results with least computational effort, as compared with other improved techniques for the trajectory optimization problem of RLV during its ascent flight. Hybrid method is then successfully used during the re-entry phase and in designing the feasible optimal trajectories under the dispersion conditions. Analytical solutions obtained from literature are used to compare the optimized trajectory during the re-entry phase. Trajectory optimization studies are also carried out for the off-nominal performances. Being a thrusting phase, the ascent trajectory is subjected to significant deviations, mainly arising out of solid booster performance dispersions. The performance index during rhe ascent phase is modified in a novel way for handling dispersions. It minimizes the state errors in a least square sense, defined at the burnout conditions ensure possibilities of safe re-entry trajectories. The optimal trajectories under dispersion conditions serve as a benchmark for validating the closed-loop guidance algorithm that is developed for the ascent phase flight. Finally, an on-line trajectory command-reshaping algorithm is developed which meets the flight objectives under the dispersion conditions. The guidance algorithm uses a pre-computed trajectory database along with some real-time measured parameters in generating the optimal steering profiles. The flight objectives are met under the dispersion conditions and the guidance generated steering profiles matches closely with the optimal trajectories.