Planning 3D Well Trajectories Using Spline-in-Tension Functions

2007 ◽  
Vol 129 (4) ◽  
pp. 289-299 ◽  
Author(s):  
J. H. B. Sampaio
Keyword(s):  
Three Dimensional ◽  
Continuous Functions ◽  
Degree Of Freedom ◽  
Additional Parameter ◽  
Gradual Change ◽  
Additional Degree ◽  
Cubic Curve ◽  
Average Curvature ◽  
End Conditions ◽  
Planning Cycle

This work presents the mathematical method to design complex trajectories for three-dimensional (3D) wells using spline in tension as coordinate functions. 3D spline-in-tension trajectories are obtained for various end conditions: free end, set end, free inclination/set azimuth, and set inclination/free azimuth. The resulting trajectories are smooth continuous functions which better suit the expected performance of modern rotary steerable deviation tools, in particular, point-the-bit and push-the-bit systems. A continuous and gradual change in path curvature and tool face results in the smoothest trajectory for 3D wells, which, in turn, results in lower torque, drag, and equipment wear. The degree of freedom and the associated parameters of the 3D curves express the commitment between the average curvature to the final length of the path that can be adjusted to fit the design requirements and to optimize the trajectory. Several numerical examples illustrate the various end conditions. This paper also presents the full mathematical expressions for the 3D path for four end conditions. The method is directly applicable to the well planning cycle as well as to automatic and manual hole steering’s. Spline-in-tension functions differ from the cubic functions in the extent that an additional parameter, which represent the “tension” of the curve, can be controlled. A totally “relaxed” curve is identical to a cubic curve, and as the tension increases a shorter curve length is obtained with a consequent effect in the curvature profile along the curve. In the limit, as the tension increases to infinite, the spline-in-tension approaches to a straight line. The tension offers an additional degree of freedom, which can be used to further optimize the final trajectory. The 3D spline-in-tension model provides the most versatile model to plan a 3D well trajectory to date. Suitable manipulation of the curve parameters, namely, L0, L1, and the three tensions, allows to give to the planned trajectory any desired behavior.

Planning 3D Well Trajectories Using Cubic Functions

2006 ◽  
Vol 128 (4) ◽  
pp. 257-267 ◽  
Author(s):  
Jorge H. B. Sampaio
Keyword(s):  
Three Dimensional ◽  
Continuous Functions ◽  
Gradual Change ◽  
Average Curvature ◽  
Expected Performance ◽  
End Conditions ◽  
Planning Cycle ◽  
Path Curvature ◽  
Lower Torque ◽  
Equipment Wear

This work presents a mathematical method to design complex trajectories for three-dimensional (3D) wells. Three-dimensional cubic trajectories are obtained for various end conditions: free end, set end, free inclination/set azimuth, and set inclination/free azimuth. The resulting trajectories are smooth continuous functions, which better suit the expected performance of modern rotary steerable deviation tools, in particular point-the-bit and push-the-bit systems. A continuous and gradual change in path curvature and tool face results in the smoothest trajectory for 3D wells, that in turn results in lower torque, drag, and equipment wear. The degree of freedom and the associated parameters of the 3D curves express the commitment between the average curvature to the final length of the path, which can be adjusted to fit the design requirements and to optimize the trajectory. Several numerical examples illustrate the various end conditions. The paper also presents the full mathematical results (expressions for the 3D path, actual curvature, and actual tool face). The method is directly applicable to the well planning cycle as well as to automatic and manual hole steering.

Designing Three-Dimensional Directional Well Trajectories Using Bézier Curves

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Jorge H. B. Sampaio
Keyword(s):  
Three Dimensional ◽  
Automated System ◽  
Hole Drilling ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Smooth Change ◽  
End Conditions ◽  
Planning Cycle ◽  
Three Space ◽  
End Set

A relatively simple, general, and very flexible method to design complex, three-dimensional hole trajectories can be obtained by using a 3D extension for Bézier curves. This approach offers superior results in terms of coding, use, and flexibility compared to other methods using double-arc, cubic functions, spline-in-tension functions, or constant curvature. The mathematics is surprisingly simple, and the method can be used to obtain trajectories for any of the four typical end conditions in terms of inclination and azimuth, namely: free-end, set-end, set-inclination/free azimuth, and free-inclination/set-azimuth. The resulting trajectories are smooth, with continuous and smooth change of curvature and toolface, better exploiting the expected delivery of modern rotary steerable deviation tools, particularly the point-the-bit and the push-the-bit systems. With the relevant parameters at any point of the trajectory (curvature and toolface angle) an automated system can steer the hole toward the defined targets in a smooth fashion. The beauty of the method is that the description of the trajectory is obtained with one single expression that handles the three space coordinates, instead of working with three separate coordinate functions. It uses a generalization of the well-known 2D Bézier curve. The concept is easy to understand, and implementation even using spreadsheets is straightforward. Besides, the conditions at both ends (coordinates and inclination/azimuth for set ends) the trajectory curve has up to two independent parameters. By playing suitably with these parameters, one can obtain a curve that favors the reduction of drag and torque during drilling, tripping, and casing running. In addition to the formulation for trajectory calculation, the paper presents the expressions to calculate the inclination, azimuth, curvature, and toolface at any point along the trajectory. Proper numerical examples illustrate the various end-conditions. The method can be used during the hole planning cycle as well as during the hole drilling for automatic and manual steerage.

scholarly journals AUXILIARY QUANTIZATION CONSTRAINTS ON THE VON ROOS ORDERING-AMBIGUITY AT ZERO BINDING ENERGIES; AZIMUTHALLY SYMMETRIZED CYLINDRICAL COORDINATES

2013 ◽  
Vol 28 (19) ◽  
pp. 1350082
Author(s):  
OMAR MUSTAFA
Keyword(s):  
Binding Energies ◽  
Degree Of Freedom ◽  
Zero Energy ◽  
Cylindrical Coordinates ◽  
Additional Degree ◽  
Quantum Numbers ◽  
Dependent Mass ◽  
Position Dependent Mass

Using azimuthally symmetrized cylindrical coordinates, we report the consequences of zero-energy quantal states on the von Roos Hamiltonian. A position-dependent mass (PDM) M(ρ, φ, z) = bzjρ2υ+1/2 is used. We show that the zero-energy setting not only offers an additional degree of freedom toward feasible separability for the von Roos Hamiltonian, but also manifestly yields auxiliary quantized ambiguity parametric constraints (i.e. the ambiguity parameters are given in terms of quantum numbers).

New Type of Two Degree of Freedom Motor Three-Dimensional Tooth Layer Field Application and Solution

2013 ◽  
Vol 391 ◽  
pp. 232-236
Author(s):  
Wen Huan Yang ◽  
Hai Xu Chen ◽  
Shuang Xie ◽  
Chun Ren Fang
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Field Application ◽  
Degree Of Freedom ◽  
Refined Method ◽  
New Type ◽  
Type Motor ◽  
Quasi Newton ◽  
Two Degree Of Freedom ◽  
Non Linear Equations

A new Multi-degree of freedom motor and its establishing of teeth layer parameters have been introduced in the paper, also including application method of database, namely using Quasi-Newton methods to solve the non-linear equations of the new motors magnetic circuit net, formed a refined method for designing and analyzing of motor. The establishment of 3d tooth layer parameters database, is provided for the calculation in the design of the new type motor conveniently.

scholarly journals Off-Design Behavior Analysis and Operating Curve Design of Marine Intercooled Gas Turbine

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Nian-kun Ji ◽  
Shu-ying Li ◽  
Zhi-tao Wang ◽  
Ning-bo Zhao
Keyword(s):  
Steady State ◽  
Gas Turbine ◽  
Optimization Design ◽  
Three Dimensional ◽  
Operational Flexibility ◽  
Modeling And Analysis ◽  
Additional Degree ◽  
Performance Space ◽  
Mechanical Constraints ◽  
Steady State Model

The intercooled gas turbine obtained by adopting an indirect heat exchanger into an existing gas turbine is one of the candidates for developing high-power marine power units. To simplify such a strong coupled nonlinear system reasonably, the feasibility and availability of qualifying equivalent effectiveness as the only parameter to evaluate the intercooler behavior are investigated. Regarding equivalent effectiveness as an additional degree of freedom, the steady state model of a marine intercooled gas turbine is developed and its off-design performance is analyzed. With comprehensive considerations given to various phase missions of ships, operational flexibility, mechanical constraints, and thermal constraints, the operating curve of the intercooled gas turbine is optimized based on graphical method in three-dimensional performance space. The resulting operating curve revealed that the control strategy at the steady state conditions for the intercooled gas turbine should be variable cycle control. The necessity of integration optimization design for gas turbine and intercooler is indicated and the modeling and analysis method developed in this paper should be beneficial to it.

Three degree of freedom description of movement of the human chest wall

1986 ◽  
Vol 60 (3) ◽  
pp. 928-934 ◽  
Author(s):  
J. C. Smith ◽  
J. Mead
Keyword(s):  
Chest Wall ◽  
Lung Volume ◽  
Pubic Symphysis ◽  
Degree Of Freedom ◽  
Rib Cage ◽  
Additional Degree ◽  
Wall Movement ◽  
Surface Displacements ◽  
Flexion Extension ◽  
Three Degree Of Freedom

A three degree of freedom description of movement of the human chest wall is presented. In addition to the standard variables representing surface displacements of the rib cage and abdominal wall in transverse planes, the description includes a variable representing axial displacements of the chest wall associated with postural movements of the spine and pelvis. A simple technique was developed for quantifying the axial displacements using a single measurement by magnetometry of changes in the distance between a point on the anterior surface of the rib cage near the xiphisternum and a point on the abdominal surface near the pubic symphysis. It was found that axial displacements produced by either flexion-extension of the spine or rotation of the pelvis in the standing postures can be treated as a single degree of freedom. The chest wall displacements induced over the range of axial displacement examined were as large as those normally accompanying a change in lung volume on the order of 30–50% of the vital capacity. It is concluded, however, that although this additional degree of freedom can cause large chest wall displacements, it probably cannot independently change lung volume. This implies that the system is constrained so that there are only a limited number of independent modes of chest wall movement that are capable of producing significant changes in lung volume. It also suggests that the system is constructed so that lung volume can be relatively independent of certain postural distortions of the chest wall.

Force-based delay compensation for hardware-in-the-loop simulation divergence of 6-DOF space contact

2017 ◽  
Vol 233 (1) ◽  
pp. 151-165
Author(s):  
Qian Wang ◽  
Chenkun Qi ◽  
Feng Gao ◽  
Xianchao Zhao ◽  
Anye Ren ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Dynamic Models ◽  
Contact Process ◽  
Three Dimensional ◽  
Compensation Method ◽  
Degree Of Freedom ◽  
Hardware In The Loop ◽  
Delay Compensation ◽  
Measurement Delay ◽  
Six Degree Of Freedom

The contact process of a space docking device needs verification before launching. The verification cannot only rely on the software simulation since the contact dynamic models are not accurate enough yet, especially when the geometric shape of the device is complex. Hardware-in-the-loop simulation is a choice to perform the ground test, where the contact dynamic model is replaced by a real device and the real contact occurs. However, the Hardware-in-the-loop simulation suffers from energy increase and instability since time delay is unavoidable. The existing delay compensation methods are mainly focused on a uniaxial or three-dimensional contact. In this paper, a force-based delay compensation method is proposed for the hardware-in-the-loop simulation of a six degree-of-freedom space contact. A six degree-of-freedom dynamic model of the spacecraft motion is derived, and a six degree-of-freedom delay compensation method is proposed. The delay is divided into track delay and measurement delay, which are compensated individually. Experiment results show that the proposed delay compensation method is effective for the six degree-of-freedom space contact.

Study on 3-D Flow Field of Concrete Volute Conduit of Circulating Water Pump in Nuclear Power Plant

2011 ◽  
Vol 99-100 ◽  
pp. 350-353
Author(s):  
Xiao Bing Sun ◽  
Xu Bin Qiao
Keyword(s):  
Power Plant ◽  
Nuclear Power Plant ◽  
Nuclear Power ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Gradual Change ◽  
Water Pump ◽  
Pump System ◽  
Circulating Water ◽  
Operating Modes

As the largest unit capacity of nuclear power plant at present, the flow conduit of circulating water pump in EPR1750 nuclear power plant is a volute conduit, which is a cast-in-situ conceret structure with complexly gradual change cavity. Therefore, the hydraulic efficiency of circulating water pump is not only related with the design of pump leaves, but also closely related to the design of volute and the complicated spatial type of intake and outtake conduits. With the pump leaves and the intake and outtake conduits of conceret volute as the research model, based on computational fluid dynamics (CFD)and the three dimensional Reynolds averaged Navier-Stokes equations, an analytic model suitable for computation is established to simulate the three-dimensional steady flow in the whole pumping system under different operating modes. By use of the commercial fluid-computation softer ANSYS, the distribution of basic physic quantities in the fluid field inside the pump and the conduits is obtained. The analysis and prediction of the performance of pump system are made, and the spatial type design of intake and outtake conduits is evaluated. The calculation results can be referenced to improve the design of pump systems in the similar projects.

scholarly journals Bogoliubov quasiparticles in superconducting qubits

2021 ◽  
Author(s):  
Leonid Glazman ◽  
Gianluigi Catelani
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Adverse Effects ◽  
Quantum Information Processing ◽  
Photon Emission ◽  
Three Dimensional ◽  
Degree Of Freedom ◽  
Superconducting Qubits ◽  
Relaxation Rates ◽  
Circuit Qed

Extending the qubit coherence times is a crucial task in building quantum information processing devices. In the three-dimensional cavity implementations of circuit QED, the coherence of superconducting qubits was improved dramatically due to cutting the losses associated with the photon emission. Next frontier in improving the coherence includes the mitigation of the adverse effects of superconducting quasiparticles. In these lectures, we review the basics of the quasiparticles dynamics, their interaction with the qubit degree of freedom, their contribution to the qubit relaxation rates, and approaches to control their effect.

scholarly journals A Note on the Properties of Generalised Separable Spatial Autoregressive Process

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Mahendran Shitan ◽  
Shelton Peiris
Keyword(s):  
Three Dimensional ◽  
Real Data ◽  
Autoregressive Process ◽  
Spatial Modelling ◽  
Spectral Density Function ◽  
Data Sets ◽  
Additional Parameter ◽  
New Class ◽  
Spatial Autoregressive ◽  
Modelling And Forecasting

Spatial modelling has its applications in many fields like geology, agriculture, meteorology, geography, and so forth. In time series a class of models known as Generalised Autoregressive (GAR) has been introduced by Peiris (2003) that includes an index parameterδ. It has been shown that the inclusion of this additional parameter aids in modelling and forecasting many real data sets. This paper studies the properties of a new class of spatial autoregressive process of order 1 with an index. We will call this aGeneralised Separable Spatial Autoregressive(GENSSAR) Model. The spectral density function (SDF), the autocovariance function (ACVF), and the autocorrelation function (ACF) are derived. The theoretical ACF and SDF plots are presented as three-dimensional figures.

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