Planning 3D Well Trajectories Using Cubic Functions (original) (raw)

Many methods have been used to calculate trajectory of horizontal and orientation well. One of effective calculation method is cubic spline interpolation function (CSIF), which calculates deviation and azimuth angle of trajectory respectively. Its present calculation function expression is based on second derivative, called three-moment equation. However, in order to obtain average borehole curvature, it has to calculate first derivative of CSIF specially. It is trouble and complicated. Another expression of CSIF, based on first derivative, called three-rotation equation, is introduced tentatively to compute borehole trajectory in this paper. While solving CSIF of deviation and azimuth angle, it is easy to calculate deviation and azimuth angle change rate and average borehole curvature. Tens of high-angle directional and horizontal wells' drilling data is computed and analyzed. The results of this study signify that the proposed method could be applied to calculate the borehole trajectory.

This paper was prepared for presentation at the 1998 SPE International Conference on Horizontal Well Technology held in Calgary, Alberta, Canada, 1-4 November 1998.

Summary A deviated well with an undersection trajectory (i.e., a trajectory lying below the conventional tangent section and constantly building to target) can exhibit lower drag and torque than a conventional well geometry in certain circumstances. The influence of well geometry on drag and torque is discussed, making use of the results of the theoretical model. Although an undersection well may have a reduced overall drag, the side forces in the drill collars will be increased. This can lead to a greater danger of sticking in the bottomhole assembly (BHA). Furthermore, because of the enhanced side forces near the bit, an undersection well may also exhibit greater torque. The relative merits of constant-build and catenary trajectories are discussed.

In the process of gradual reorientation of the oil industry to the production of heavy hydrocarbons, inaccessible to traditional methods of production, the need arises for the application of modern technological solutions. One of these technologies is directional drilling, which poses new challenges for drilling equipment, such as facilitating sliding - changing the angle of well bore, improving the cleaning of the wellbore, reducing the risks of differential sticking, overcoming resistance during horizontal drilling, etc. A modern technological solution is rotary steerable systems (RSS) representing a new generation of downhole systems used in directional drilling. The article discusses the advantages and disadvantages of RSS technology, its modifications, gives a classification, also provides a comparative analysis of well wiring using rotary steerable systems and, the most widely used, mud motor.

The most important aim in tool path generation methods is to increase the machining efficiency by minimizing the total length of tool paths while the error is kept under a prescribed tolerance. This can be achieved by determining the moving direction of the cutting tool such that the machined stripe is the widest. From a technical point of view it is recommended that the angle between the tool axis and the surface normal does not change too much along the tool path in order to ensure even abrasion of the tool. In this paper a mathematical method for tool path generation in 3-axis milling is presented, which considers these requirements by combining the features of isophotic curves and principal curvatures. It calculates the proposed moving direction of the tool at each point of the surface. The proposed direction depends on the measurement of the tool and on the curvature values of the surface. For triangulated surfaces a new local offset computation method is presented, which is suitable also for detecting tool collision with the target surface and self intersection in the offset mesh.

The main objectives in a successful drilling operation is to construct safe and economically efficient wells, but this success depends on hitting the target. As the drilling operation have very high standards of execution, a good drilling operation depends on a good well plan. Well trajectory planning is a mixture of many parameters but in the end it comes down to identifying the most optimum well path. This has to do with using exact mathematical calculation models, to precisely calculate well bore trajectories. This thesis investigates the concept of directional drilling , its application coupled with the derivation of mathematical equations built using trigonometry functions to code for the type 1 (j well) profile, and finally a graphic user interface (gui) integrated developer program was used to build a desktop application called WELLPLANNER based on the algorithm generated. This application was used to simulate different conditions by carrying out a sensitivity analysis of the various input parameters in the Software. Furthermore, a general equation was generated and resolved using the Formula method of solving quadratic equation, and this could be used to predict the value of build-up rate when it is unknown for a new field.