A Microcomputer Program for Prediction of Bottomhole Assembly Trajectory

Abstract

Summary. This paper describes a two-dimensional (2D) static, finite-element microcomputer program capable of quantitatively predictin the inclination behavior of bottomhole assemblies (BHA's). A calculation module that is based on the finite-element method helps account for the forces generated between the components of the BHA and the wellbore wall. This module is used in an automatic iterative process to compute the "equilibrium curve" of the BHA, which gives the future inclination gradient of drilling. The analysis of horizontal wells drilled by Elf Aquitaine demonstrated the role played by the hole-diameter-enlargement/ rate-of-penetration (ROP) relation in prediction improvements. Introduction Drillers confront the problem of borehole deviation every day either in vertical wells, where deflection should be minimal, or in directional wells where the bit course has to be controlled all along. One of the key problems faced by drillers is to select conveniently the components of the BHA for an optimum inclination behavior. This problem is generally approached in reverse by finding ways to problem is generally approached in reverse by finding ways to predict the inclination behavior of the BHA. The solution depends predict the inclination behavior of the BHA. The solution depends on various factors, such as BHA components; drilling parameters, including weight on bit (WOB), mud weight, and rotary speed; well data including well path and hole size: and the formation characteristics, including heterogeneity, anisotropy, and dip. Since Lubinski, a pioneer on the subject, published his first works, many mathematical models of BHA have been developed. These models help to calculate the side force exerted on the bit and to obtain a qualitative knowledge of the working direction of the BHA from this information. They are either 2D or three dimensional (3D) and either static or dynamic. Most 2D models use an analytic approach. Calculation is very rapid, but model capabilities are limited. Not all types of BHA's can be modeled (there must be a limited number of stabilizers and drill collars with the same diameter). The borehole must feature a rectilinear or a constant-curvature profile. The 3D models generally use the finite-element method for BHA modeling. As a result, all types of BHA and wellbore profiles can be modeled, but calculation time is quite long. Calculations can take up to 1 hour on big vector computers, especially for dynamic models that take rotary speed into account. The mathematical model discussed here, ORPHEE 2D, falls between these two types. It is a 2D static model that uses the finite-element method. All BHA's can be modeled. Calculating time is short enough for the program to run on a microcomputer and to be used on the rig easily. One of the main characteristics of ORPHEE 2D is that two types of data can be obtained:the side force on the bit, allowing a qualitative prediction of the build/drop tendency, andthe equilibrium curvature of the BHA, allowing a quantitative prediction of the course of the BHA. Additionally, some formation effects are taken into account through the ROP, which is used to determine the hole-size increase in the course of drilling. In this paper, we first describe the program structure, which includes the side-force calculation module and equilibrium-curvatur determination. Use of the equilibrium-curvature method is justified by the small effect of the borehole inclination at the bit. We then compare model predictions and field results, pointing out the effect of borehole enlargement on model predictions, how enlargement is determined from the ROP, and the prediction improvements to be expected. Finally, we present the characteristics of the program that make it a user-friendly tool. program that make it a user-friendly tool. Program Structure Program Structure Side-Force Calculation Module. ORPHEE 2D includes a calculation module based on the finite-element method (see the Appendix). It determines the inclination side force on the bit from the BHA components, well data (inclination measurements and hole size), and drilling parameters (WOB and mud weight). This is not sufficient, however, to make a quantitative prediction of the inclination behavior of a BHA. The evaluation of the build/drop tendency is only qualitative, and this qualitative evaluation is not reliable. For example, the inclination side force applied by a buildup assembly may be directed downward in a highly and upwardly curved well (because of the BHA previously used). Therefore, the result is not representative of the long-term behavior of a buildup assembly, which eventually will be directed upward. The Equilibrium Curvature Method. To depart from the "memory effect" of the last meters drilled and also to make a quantitative prediction of the course of the borehole, the calculation module is used in an automatic iterative process to determine the equilibrium curvature of the BHA. We started from the assumption that the BHA's operation decreases the side force on the bit. When this force is reduced to zero, the wellbore curvature is constant. We caned this curvature the equilibrium curvature of the BHA. It can be calculated by the following method. Consider the BHA to be run in a fictitious well with a constant curvature and an inclination angle at the bit equal to that of the real well. Then, determine the fictitious-well curvature required to reduce the side force on the bit to zero. To do this, an iterative process (linear-interpolation method) is applied to the side-force process (linear-interpolation method) is applied to the side-force calculation module by changing the radius of curvature of the well until the side force equals zero. Effect of Bit Inclination. Actually, should the inclination effect be significant, the equilibrium curvature would quickly change with footage, thus making the equilibrium concept meaningless. Fig. 1 shows the equilibrium curvature vs. inclination at the bit for the three types of BHA's shown in Fig. 2: buildup assembly, lockup assembly, and dropoff assembly. As Fig. 1 shows, inclination at the bit has little effect on the equilibrium curvature. For example, the equilibrium curvature for a lockup assembly varies from 0.003 to 0.004 rad/10 m [0.006 to 0.007 deg. /ft] when inclination varies from 0.44 to 0.96 rad [25 to 55 deg. ]. These data justify the equilibrium-curvature concept. Comparisons With Field Results- Model Adjustment In this section, we show that well-path predictions based on a hole size equal to the bit size can be substantially improved by increasing the hole size. We show, too, that borehole enlargement, which is not measurable while drilling, can be approximated from the ROP. P. 167