Finite Element Modeling of the Mechanical Behavior of Unbalanced Drillcollars
Authors: de S.M. Costa F. , Ribeiro P.R. 
Published: December 2007

Abstract
This work treats the finite element modeling of the mechanical behavior of BHAs equipped with unbalanced drillcollars. The assembly was discretized in 2-D beam-column elements and the geometric non-linear problem was handled by Newton's method with an incremental loading scheme. The model was validated by some classical large displacement and small deformation beam problems as well as published data for the static behavior of stabilized drillcollars. The constraint imposed by the borehole walls was implemented by bilinear spring elements. The analysis of the variation of the magnitude of the reaction force at the bit, due to drillstring rotation, was performed by applying a body force to the BHA which was equivalent to the unbalanced force. This kind of approach allowed a simplified treatment of the dynamic behavior of the system in a static point of view. The effect of the unbalanced force in the reaction force at the bit was investigated and an effective tendency of reducing inclination of the wellbore was verified, with an increasing rotational speed of the drillstring.

Introduction
The control of the trajectory of the well during drilling is an important issue in the petroleum exploitation, as it is closely related to the overall cost of the operation. Keeping the well close to the designed trajectory and applying the correct drilling parameters (weight-on-bit, rotational speed and drilling fluid flow rate) will allow to reach the target in a reduced time frame, avoiding any sort of intervention for correction of the trajectory.
Due to the geological characteristics of certain fields, there is a natural tendency of gain of inclination of the well during drilling, what causes the undesired deviation from designed vertical trajectory. This kind of problem is quite frequent in the Jacuipe area of the Reconcavo Balano basin (Brazil), and significant effort has been made to reduce the costs associated with the maintenance of the vertical trajectory of developing wells.
There are, basically, two ways to maintain the vertical trajectory of the well:
- using a stabilized drillstring;
- using a BHA equipped with unbalanced drillcollars.
The stabilized drillstring option requires the placement of stabilizers at strategic points along the BHA, which will alter the orientation of the bit due to the reaction in the contact points between the drillcollars and the borehole. Despite the satisfactory results obtained with this option, there is a significant increase in the torque and drag in the drillstring.
The principle of operation of the unbalanced drillcollars is based on the centrifugal force effect due to drillstring rotation, that generates a reaction force at the bit which tends to maintain the vertical trajectory of the well. The unbalance is attained by machining a sequence of holes along the drillcollars. The unbalanced drillcollars were firstly used to drill exploratory wells in regions with tendency of gain in inclination in the U.S.A. and also to increase the rate of penetration in some fields in Kansas and Wichita. The usage of unbalanced drillcollars has also proven to be the most cost-effective option in the Reconcavo basin: maximum inclinations of 6 were registered by using unbalanced drillcollars, where inclinations up to 13 had been measured by using conventional drillcollars. These results encouraged the usage of the tool in more than half of the wells drilled in that area and also began raising questions regarding some technical aspects of the application, such as:
- magnitude of the reaction force at the bit caused by the unbalance;
- displacement of the drillcollars downhole
- comparison of the mechanical behavior of the drillstring equipped with stabilizers or unbalanced drillcollars.
Due to the inherent difficulties of measuring the quantities which would help answering any question related to the behavior of the drillstring downhole, a finite element model has been developed to simulate the static behavior of the drillstring.