3D Drill String Mechanics Algorithm And Its Software Development

The drilling engineering, a vita part of oil exploitation, involves a great deal of complicated engineering problems, such as the hole deviation control, the prediction of string buckling, and the vibration of drill string, which require the insight of mechanics. As the important theoretical foundation of drilling engineering, drill string mechanics provides a mathematical abstraction of the drill string down hole, thus promoting the understanding of the problems encountered in the engineering field. After many years of development, a lot of drill string models and corresponding algorithms were proposed. These models and algorithms successfully solve many problems in the oil field, while each of them has its own shortcoming. The purpose of this paper is to develop a new drill string mechanics algorithm, based on the static mechanics, and develop software to analyze the drill string mechanics problems.The basic equations of drill string mechanics are studied and some currently prevailing drill string mechanical models are compared. For all models, the computation of the contact force is very important, but each of them has a different way of solving the contact force. The traditional models consider that the drill string lies on the lower side of the hole. The models are very simple and work successfully in most of the applications in the oil field, while reporting bad results in a few conditions. However, they are too simple to be satisfactory on some occasions. Therefore, the treatment of the contact forces needs to be improved. In this paper, the contact force is regarded as the result of the deformed drill string contacting the well. Starting with the basic equations of drill string mechanics, the deformation of drill string down hole is studied. In order to find out how the contact forces impact the deformation of drill string, the relation between the contact force and the displacement of a single node is established which uses the equilibrium equations and the elastic equations to generate the deformation equations of a single node. After deformations are determined, the method of computing the contact forces on a single node is derived. Then, the relation for a single node is generalized to all nodes of the entire drill string, and a new method of computation is proposed. The contact feedback is used in both Finite Element Method(FEM) and ABIS method to compute the contact force. The convergence time used in FEM is longer than that of ABIS. However, the convergence performance of ABIS becomes poor, when processing drill string with length close to 3 kilometers. The flexible matrix method is introduced, in this paper, to iterate the contact force using the relationship between contact force and displacement, which makes the operation of adding a contact force more easily. Further, a new algorithm of drill string mechanics is proposed— FMDS(Flexible Matrix Drill string), based on the research of the computation of contact force, and an open source math matrix library, called MTL(Matrix Template Library), is chosen to implement the algorithm.Inasmuch as the enormous time consumed on the computation of flexible matrix, the parallel algorithm is employed to study the flexible matrix algorithm, based on the parallel computation. As the size of the flexible matrix is determined by quantity of drill string nodes, the longer the drill string is, the more the nodes there are, thus resulting in bigger matrix, which means the computation time will be longer. Because of the unique mathematical structure of flexible matrix, its process is naturally parallelizable. A parallel matrix algorithm is developed for the flexible matrix in the contact iteration, using OpenMPI, an open source platform, and the parallel block in MATLAB.A software with 3D drill string mechanics analysis is developed under the new graphic user interface framework from Microsoft, called Windows Presentation Foundation. With the FMDS integrated, the horizontal directional drilling mechanics software, providing mechanics analysis support, drill string design, and well track visualization, is developed, in which there are three blocks:preprocessing block, computation block, postprocessing block, regarding to the requirement in the drilling engineering field.Based on the real well trajectory data from the field, an example of application of FMDS is given, along with other different algorithm. In comparison of these algorithms, it is found out that the results of FMDS and stiff string model are very close, when the string haven’t reached the helical buckling; it is also displayed that their results show significant difference when the string enters the helical buckling. Comparison with ABIS, FMDS shows a better performance in terms of time consuming, while having similar results to ABIS, especially when it comes to the length of 3 kilometers drill string.This paper comes to several conclusions. Firstly, it is demonstrated that the simplification of drill string in traditional drill string model, such as soft string model and stiff string model, presents contradiction and problems in certain cases. On the one hand, the assumption that the string lies on the lower side in the well, is not appropriate in some cases, because there is a situation that the string may contact the upper side of the well. On the other hand, mending the contact force according to the axis force leads to conservative results. Due to the absence of contact algorithm, the stiff string model revises all nodes’contact forces as long as the axis forces reach the critical buckling value, regardless of whether the node contacts the well. As a consequence, the results of axis force are generally greater than the real ones. Secondly, the iteration speed of FMDS is faster than ABIS. In the process of searching contact points, the iteration speed can be improved, using a more flexible way of adding contact points, with the applying of flexible matrix.