Modeling of Complex Bottom Hole Assemblies in Curved and Straight Holes

Authors: S. Miska, W. Miska

In horizontal and directional drilling operations a drilling engineer is always faced with issues related to designing the elements of bottom hole assemblies to achieve the planned directional well path. A fundamental question here is how to select the composition of the BHA so that the drillbit will penetrate the rocks in the desired direction.

This is usually accomplished by assuming the composition of the BHA and then calculating the side force at the drillbit. Once the side force is known one can predict the direction and magnitude of the resultant force at the bit and hence the anticipated instantaneous bit displacement. Therefore the oil/gas industry has a strong interest in studies that permit better predictions of BHAs.Following the fundamental studies of Arthur Lubinski a number of authors proposed various techniques for handling this problem. Detailed analysis of the literature in this area can be a subject of a separate paper. More important papers are listed at the end of the paper.

An effective technique for determining the static equilibrium configuration of complex (including various sizes of drill collars, down – hole motors, stabilizers and bent subs) bottom hole assemblies (BHAs) in curved and straight holes is presented in this paper. The technique is based upon a concept of transfer matrix that is widely used by structural engineers for analyzing complex configurations of elastic beams. This technique permits to find the equilibrium shape of the BHA and forces at the drill bit and all points of contacts with the well bore wall for given geometry of BHA and working conditions. In general, BHA consists of a number of mechanical elements, including various types of drill collars, down hole motors, MWD units etc. of given geometrical and mechanical properties. It is also possible that some of these elements can be initially curved rather than straight.

To achieve the desired directional drilling performance (building, holding and dropping tendencies), various stabilizers and bent subs are used in addition to the above-mentioned components. The assembly is laterally constrained by the walls of the borehole. The borehole itself can be geometrically straight or curved.

The working conditions are specified by a hole size and geometry (straight, curved or some combinations of both straight and curved segments), weight on bit, drilling fluid density etc.The main purpose of this paper is to provide a theoretical background for the proposed transfer matrix approach for analyzing complex BHAs.