Basic Concepts in Static BHA Analysis for Directional Drilling

Abstract

Abstract Basic concepts related to the static analysis of two- and three-dimensional bottomhole assemblies are discussed. Beginning with a straight one stabilizer assembly, the effects of multiple stabilizers, borehole curvature, torque, wall contact, etc. are introduced in steps. The criteria for defining the build, hold, drop and walk trends is clarified. Two methods for computing bending stiffness and equivalent outer diameter of MWD collars with nonuniform cross-sectional properties are proposed, Also, simple methods of estimating buckling loads for one and two span assemblies are presented. Introduction In the early days of drilling, the holes were shallow and were supposedly drilled straight. The experience with the Seminole fields in Oklahoma during the late twenties, made the industry realize that drilling does not necessarily follow the intended trajectory. Something happens downhole which makes the drillstring deviate from its course. The efforts to understand the cause for deviation of drillstrings led to their mechanical analysis using the concepts of structural mechanics. Many papers have been written on the subject. However, the basic concepts of mechanics, as related to directional drilling, have not been put together in a systematic manner. This paper attempts to fill such gap. paper attempts to fill such gap. The subject matter in this paper is presented on the lines of standard textbooks on structural mechanics Herein, a BHA (bottomhole assembly) is treated as a beam column subjected to its self-weight, buoyancy, and weight-on-bit (WOB). For simplicity, a one stabilizer BHA in a straight but inclined borehole is discussed first. Then, further considerations of multiple stabilizers, borehole curvature, torque, wall contact and of variations in collar cross-section or material properties are introduced in steps. Both two- and three-dimensional BHAs are discussed. The difficulties experienced in the application of closed from methods, and the advantages of their numerical counterparts (finite difference and finite element) in analyzing complex modern BHAs are highlighted. Then, using the equilibrium of forces at the drill bit and the formation, the criteria for defining the build, drop, hold and walk trends is explained. Since bending is the dominant mode of deformation in a drillstring, the knowledge of its resistance to bending, i.e. bending stiffness, is important. This paper explains the basic concepts of stiffness and presents two methods for computing bending stiffness and equivalent diameter of collars with non-uniform cross-section (e.g. MWD collars). Finally, simple methods for estimating critical buckling loads of bottom hole assemblies are discussed. The scope of the paper is limited to the static analysis of the drillstrings. It does not discuss the effect of dynamics or of rock and bit characteristics on the directional tendencies of BHAs. Also, it emphasizes combining the physical and mathematical concepts in a simple fashion. No attempt is made to provide mathematical derivations; instead, the applicable expressions are borrowed from easily accessible sources.