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.

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.

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.

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 Dynamic target template matching for railway catenary suspension motion detection in wind area

2018 ◽  
Vol 14 (9) ◽  
pp. 155014771879795 ◽  
Author(s):  
Wei Zhou ◽  
Heting Xiao ◽  
Zhonggang Wang ◽  
Lin Chen ◽  
Shaoqing Fu
Keyword(s):  
Template Matching ◽  
Three Dimensional ◽  
Moving Target ◽  
Maximum Relative Error ◽  
Gradual Change ◽  
Matching Method ◽  
Safety Research ◽  
Target Template ◽  
Target Templates ◽  
Dynamic Target

A dynamic target template matching method was proposed to identify railway catenary suspension movements of wind-induced vibration in wind area. Catenary positioning point was taken as the target template, which was compared with equal-sized image sequentially using the proposed matching difference. And, three-dimensional contour map of matching difference value at each sub-area was obtained, where the target pixel coordinates were determined by the minimum matching difference value. Considering the complex imaging condition, the target template was updated by the detected target image to sense the gradual change of illumination conditions like brightness and contrast. Furthermore, to eliminate detecting errors due to wind-induced camera vibration, both static and moving target templates were identified for acquiring the absolute motion of the moving target. Finally, validation test was performed with animation in PowerPoint. The calculated target displacement agrees well with theoretical motion with maximum relative error of 1.8%. And experiment application was conducted at site by analyzing the relationship between detecting displacement and wind speed. Results indicate that the proposed dynamic target template matching method can meet required engineering precision and provide an effective way for wind-vibration safety research of railway catenary system in wind area.

Contact Stress Reduction Mechanisms for the CAM-Based Infinitely Variable Transmission

2007 ◽  
Author(s):  
Derek F. Lahr ◽  
Dennis W. Hong
Keyword(s):  
Contact Stress ◽  
Stress Reduction ◽  
Kinematic Model ◽  
Three Dimensional ◽  
Speed Ratio ◽  
Cam Mechanism ◽  
Expected Performance ◽  
Differential Mechanism ◽  
Variable Transmission ◽  
Infinitely Variable Transmission

The Cam-based Infinitely Variable Transmission (IVT) is a new type of ratcheting IVT based on a three dimensional cam and follower system which provides unique characteristics such as generating specific functional speed ratio outputs including dwells, for a constant velocity input. This paper presents several mechanisms and design approaches used to improve the torque and speed capacity of this unique transmission. A compact, lightweight, and capable differential mechanism based on a cord and pulley system is developed to double the number of followers in contact with the cam at any time, thereby reducing the contact stress between the followers and the cam surface considerably. A kinematic model governing the motion of this differential is developed and a few experimental results from the prototype are presented, showing an overall increase in performance including a smooth output, a wide gear range, and the ability to shift under load. Plans for future improvements to the design, including an inverted external cam mechanism, is also presented along with the expected performance gains.

The Identification of the Potential Limitations of Acoustic Rhinometery Using Computer-Generated, Three-Dimensional Reconstructions of Simple Models

1996 ◽  
Vol 10 (2) ◽  
pp. 77-82 ◽  
Author(s):  
A. Tomkinson ◽  
R. Eccles
Keyword(s):  
Nasal Cavity ◽  
Three Dimensional ◽  
Internal Surface ◽  
Three Dimensions ◽  
Gradual Change ◽  
Large Area ◽  
Cross Sectional ◽  
Wave Path ◽  
Acoustic Evaluation ◽  
Set Up

The internal surface of the nasal cavity is geometrically complicated and does not lend itself readily to direct measurement. Simple geometric shapes were used as a model for changes in the nasal cavity. Following the introduction of specific changes to a particular system, the effect of these changes on the acoustic evaluation of the space was studied. Cylinders were chosen, as the wave path could be assumed to be perpendicular to the model surface. The acoustic rhinometer's accuracy was assessed in the presence of small and large variations in cross sectional area, in the presence of a series of consecutive area changes, and a gradual change in diameter. The effect of the introduction of acoustic leak was also modelled. The acoustic data acquired from these models was used to reconstruct the model in three dimensions. These reconstructions were compared to the original model. The acoustic rhinometer was found to resolve with reasonable accuracy the dimensions of small spaces; however, if regions of sudden large area changes were present in the space, the data beyond these regions was highly unreliable. Furthermore, the presence of acoustic leak in a system had a similar effect. Unless precautions are taken in the set-up and operation of the acoustic rhinometer, the potential for misinterpretation of data and the introduction of bias is very high.

Preliminary Results of Numerical Simulations of a Bio-Mimetic Wells Turbine

2016 ◽  
Author(s):  
Qiuhao Hu ◽  
Ye Li ◽  
Fangyi Wei
Keyword(s):  
Energy Conversion ◽  
Three Dimensional ◽  
Turbine Rotor ◽  
Navier Stokes ◽  
Maximum Efficiency ◽  
Wells Turbine ◽  
Turbulence Effects ◽  
Dimensional Simulation ◽  
Lower Torque ◽  
Good Agreement

Wells turbine is a kind of self-rectified air turbines used in an oscillatory water column (OWC) device for wave energy conversion. In this study, a steady three-dimensional simulation of a fan-shaped Wells turbine is performed on Star CCM+ commercial software by solving the Reynolds-averaged Navier-Stokes (RANS) equations. The turbulence effects are taken into account by using the Spalart-Allmaras turbulence model. Good agreement between the numerical results and the experimental results within the operation region (5< α <11 degrees) is observed. The geometry of the turbine rotor has a significant effect on the performance of energy conversion. Inspired by the aerodynamics of low Reynolds flyer, the normal fan-shaped Wells turbine is optimized by a bio-mimetic method in which the profile of a hawk moth wing of Manduca Sexta is applied on the blades. The modified turbine has a lower torque and pressure drop coefficient with higher efficiency. The maximum efficiency for the modified turbine is 0.61, compared to 0.48 for the normal fan-shaped one. By analysis of the detailed flow-field, it has also been found that only the middle parts of the blade can effectively generate the momentum. In order to acquire a higher efficiency, further optimization is carried out by refining some blade parts in the tip and the hub which cannot effectively produce power.

Postural Control of Three-Dimensional Prehension Movements

1997 ◽  
Vol 77 (1) ◽  
pp. 452-464 ◽  
Author(s):  
Michel Desmurget ◽  
Claude Prablanc
Keyword(s):  
Postural Control ◽  
Upper Limb ◽  
Three Dimensional ◽  
Joint Space ◽  
Object Orientation ◽  
Task Space ◽  
Movement Onset ◽  
Dynamic Level ◽  
Prehension Movements ◽  
Path Curvature

Desmurget, Michel and Claude Prablanc. Postural control of three-dimensional prehension movements. J. Neurophysiol. 77: 452–464, 1997. This experiment was carried out to test the hypothesis that three-dimensional upper limb movements could be initiated and controlled in the joint space via a mechanism comparing an estimate of the current postural state of the upper arm with a target value determined by one specific inverse static transform converting the coordinates of the object into a set of arm, forearm, and wrist angles. This hypothesis involves two main predictions: 1) despite joint redundancy, the posture reached by the upper limb should be invariant for a given context; and 2) a movement programmed in joint space should exhibit invariant characteristics of the joint covariation pattern as well as a corresponding variable hand path curvature in the task space. To test these predictions, we examined prehension movements toward a cylindrical object presented at a fixed spatial location and at various orientations without vision of the moving limb. Once presented, the object orientation was either kept constant (unperturbed trials) or suddenly modified at movement onset (perturbed trials). Three-dimensional movement trajectories were analyzed in both joint and task spaces. For the unperturbed trials, the task space analysis showed a variable hand path curvature depending on object orientation. The joint space analysis showed that the seven final angles characterizing the upper limb posture at hand-to-object contact varied monotonically with object orientation. At a dynamic level, movement onset and end were nearly identical for all joints. Moreover, for all joints having a monotonic variation, maximum velocity occurred almost simultaneously. For the elbow, the only joint presenting a reversal, the reversal was synchronized with the time to peak velocity of the other joint angles. For the perturbed trials, a smooth and complete compensation of the movement trajectory was observed in the task space. At a static level the upper limb final posture was identical to that obtained when the object was initially presented at the orientation following the perturbation. This result was particularly remarkable considering the large set of comfortable postures allowed by joint redundancy. At a dynamic level, the joints' covariation pattern was updated to reach the new target posture. The initial synergies were not disrupted by the perturbation, but smoothly modified, the different joints' movements ending nearly at the same time. Taken together, these results support the hypothesis that prehension movements are initiated and controlled in the joint space on the basis of a joint angular error vector rather than a spatial error vector.

The Influence of Long-Range Residual Stress on Plastic Collapse and Local Yielding of Internally Pressurized Pipes

2012 ◽  
Author(s):  
Gui-yi Wu ◽  
D. J. Smith ◽  
M. J. Pavier
Keyword(s):  
Residual Stresses ◽  
Long Range ◽  
Structural Engineering ◽  
Three Dimensional ◽  
Plastic Collapse ◽  
Displacement Control ◽  
Integrity Assessment ◽  
End Conditions ◽  
Global Collapse ◽  
Local Yielding

The determination of plastic collapse for cracked pipes is important in structural engineering design and component integrity assessment. Long-range residual stresses are usually treated as primary stresses which contribute to plastic collapse of pipes subjected to internal pressure. This paper explores the differences between load and displacement controlled conditions applied to the ends of thin- and thick-walled pipes. Both load and displacement control can represent long range or fit-up residual stresses if they are considered as primary or secondary stresses respectively. Both global collapse and local yielding for pipes containing partially and fully circumferential cracks are examined. Detailed three-dimensional (3D) finite element (FE) analyses are used to simulate the pipe and crack geometry and the boundary conditions. The cracked pipes are assumed to be open ended. For a defect free pipe the FE results for global collapse agree with analytical solutions for both load and displacement controlled end conditions. For high tensile end loads and displacements lower collapse pressures are found for displacement conditions, while it is the converse for high compressive end loading. However, when a crack is introduced it becomes evident that tensile or compressive displacement control has little impact on global collapse and therefore longrange displacement controlled (or residual) stresses do not contribute to collapse. On the other hand local net section yielding is strongly affected by either load or displacement controlled end conditions.

Physiological Interaction, Its Mathematical Expression

Weed Science ◽  
1980 ◽  
Vol 28 (5) ◽  
pp. 573-579 ◽  
Author(s):  
Robert E. Drury
Keyword(s):  
Three Dimensional ◽  
Mathematical Expression ◽  
Continuous Functions ◽  
Fresh Weight ◽  
Regression Estimate ◽  
Independent Variables ◽  
Algebraic Expressions ◽  
Independent Variable ◽  
Two Parameter ◽  
Two Independent Variables

The concept of interaction arises in the context of continuous functions. Verbally, it is the action of one independent variable on the action of another, and vice versa, on a dependent variable. Quantitatively, it is the second partial derivative of a function with respect to two independent variables. Misconceptions have arisen from attempts to understand action and interaction in discrete terms. The algebraic expressions for the actions of diuron and phorate on the fresh weight of oats and their interaction were determined from the regression polynomial and plotted in three-dimensional graphs. Three other mutually incompatible methods of assessing interaction, namely, the Colby (with its modification, regression estimate), the two-parameter, and the topographical methods were evaluated.

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