Dynamic Analysis of BHA with Bent Housing
Authors: Jianhong Fu , Shi Taihe 
Published: December 2007

Abstract
During horizontal well drilling, to reduce buildrate or drill the holding section, the drillstring should be rotated, so it is necessary to study dynamic performances of the boftomhole assembly (BHA) with bent housing. Based on finite element theory, this paper presents dynamic model to study the effects of rotary speed, WOB, bent angle and inclination on dynamic characteristics of BHA with bent housing. By full transient simulation, we obtained side force on the bit varing with the time, tilt angle of the bit varying with the time and orbital path of arbitrary traverse section along the drillstring.
Dynamic simulation results can be used to select proper drilling parameters, drillstring configuration in order to control trajectory of horizontal wells and prevent drillstring fatigue failure. 3 medium radius horizontal wells were drilled in Karamay oilfield in China by using our research results.

Introduction
Dynamic analysis of BHA's is used for vertical wells, directional wells, and horizontal wells. For a vertical well, the applications of dynamics of BHA's is mostly to prevent fatigue failure of drillstring1. For directional wells and horizontal wells, dynamic analysis focuses on the bit side force and motion status of BHA2,3, which greatly affect trajectory of directional and horizontal wells.
Generally vibration of drillstrings is the combinations of three basic modes: axial, lateral and torsional vibrations, these three vibrations are not independent under certain circumstance, one mode can affect the others, on the other hand, the deflection of drillstring is constrained by wellbore, which cause friction between drillstring and wellbore, and surface and downhole boundary conditions have great effects on dynamic behavior of drillstring4, all these factors make drillstring dynamic analysis very complicated. Although great simplifications and many assumptions are made, full transient simulations of BHA with multi-freedom degrees is not easy to solve, so a number of researchers apply harmonic analysis using finite element5,6,7,8 to calculate lateral displacement, stress and nature frequency, basic principles of harmonic analysis is to apply monochromatic harmonic force vector excitation at the bit, and to assume that the frequency of dynamic response of BHA is the same as the frequency of forced frequency, then dynamic model is transferred into a frequency-dependent quasi-static model.
Besides finite element analysis of BHA, analytical method was also used to determine motion status and critical speed of BHA9,10,11 by using anytical method, drillstring whirling and liner coupling between WOB and lateral vibration can be analyzed. These researches show that forward whirl results in drill collar wear and backward whirl leads to fatigue. During normal drilling operations, both forward whirl and backward whirl of BHA in the borehole may take place.
Drill collar inevitably moves to contact with wellbore and then bounces, but so far, bouncing motion status remain unclear, Jansen12 set up nonlinear motion equation of middle traverse section between two stabilizers, simulated bouncing motion of drillcollar, in this case, critical speed decreases as clearance of stabilizers increases. When clearance between stablizer and wellbore exceeds mass eccentricity. It is almost impossible for forward synchronous whirl to occur.
Field vibration measurement were also carried out in several oilfields, and measurement instruments and data analysis have made a great progress, these work are very useful to improve theoretical dynamic models of BHA.