BHA Behavior-Prediction Model Offers Potential for Automated Analysis

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A new 3D drillstring model determines the static and dynamic behavior of bottomhole assemblies (BHAs) in realistic wellbores. The modeling approach provides a prediction of the BHA’s mechanical and dynamic behavior and can be used as a planning tool for BHA design, an investigative tool for root-cause analysis, or, potentially, as a real-time optimization tool for avoiding harmful operating conditions.


When using any model, engineers cannot forget the limits of calculation. However, they can settle for “good enough” as long as they adhere to the following two rules:

  • The results capture the general behavior of the system with respect to the parameters of interest.
  • The engineer using the results fully understands the limits of the model used to obtain them.

These rules are particularly important when considering highly nonlinear systems, such as the 3D behavior of BHAs. Nonlinearity arises in these systems from the large, coupled deflection that occurs in the downhole components as they move within the wellbore, and the frictional contact that results from the borehole wall restraining that movement. These inherent complexities have been a driving factor for continued research on the subject of BHA modeling for years. On the basis of the author’s own investigative studies and working experience, there appear to be three primary areas of focus within the study of BHA mechanics and dynamics:

  • The mechanical loading on the downhole components
  • The directional performance of various drilling assemblies
  • The dynamic response of BHAs

The purpose of the current project was to develop a BHA model that could analyze each of these topics in an efficient manner while maintaining a reasonable level of accuracy. Such a model could then be leveraged routinely to design more-robust tools and provide a reliable approach to engineering support for drilling operations.

BHA Simulation Model

As a response to the need to estimate downhole performance better, a mathematical model has been developed for estimating the mechanical and dynamic behavior of BHAs in realistic wellbores. It is based on a nonlinear finite-beam element and accounts for various intricacies of the downhole environment. Modeling a drilling assembly using this approach allows for the complexities of the BHA components to be easily represented as a series of beams with varying mechanical properties. The model was initially developed to analyze the behavior of vibration-­inducing devices in unconventional horizontal wells, but has since been expanded to examine a multitude of different drilling scenarios.

The complete paper offers a summary of the model. Within the structure of the developed program, the BHA is represented by a system of nonlinear partial differential equations presented there. In general, three types of analyses can be performed on the basis of this system of nonlinear equations: quasistatic deflection (mechanical loading), estimates of the dynamic response in the frequency domain (linearized vibration), and fully nonlinear simulations in the time domain.

The emphasis of the present work is to explore the applicability and practicality of the linearized calculation methods (quasistatic and linearized-dynamic analysis) and show their effectiveness at addressing real-world scenarios.

Model Validation

The process of model validation is discussed in detail in the complete paper. The validation data presented there have been gathered from different sources during a 2-year period, with some acquired during dedicated field trials at a test facility in Oklahoma and other data stemming from commercial operations in the Marcellus, Woodford, and Permian Basin. Aspects of model validation included

  • Mechanical loading
  • Measurement of lateral natural frequencies of the BHA
  • Torsional natural frequencies (high-frequency torsional oscillations)
  • Directional performance

Case Studies

The validated model has been used in support of operations around the globe for pre-well planning and as a tool for root-cause analysis. In addition to directional performance comparisons, three case studies that highlight the practical application of the model are presented in the Appendices of the complete paper. They are briefly summarized here:

  • While drilling an intermediate hole in west Texas, damage to an 8-in. steerable mud motor was experienced. Mechanical-loading and vibration analysis helped identify the cause of fatigue-related damage to its internal components. Mechanical loading revealed that the highest bending loads in the BHA occurred at the location at which the damage was observed, while vibration analysis showed that the BHA was being operated close to a resonant flow rate (resonance induced by the rotor whirl within the motor), which added a significant dynamic bending load to the already loaded motor. This ultimately led to the fatigue-related damage observed on the motor’s mandrel.
  • Redesign of an instrumented motor provided increased tool reliability and decreased sliding times while drilling steam-injection wells in Canadian heavy-oil sands. An instrumented motor was experiencing excessive vibrations and notable wear downhole. The BHA/motor being used would build too much during rotation and require excessive corrections while drilling the lateral section of the well. Mechanical-loading analysis indicated that the vibration was likely the result of intermittent contact (repetitive impact loading) between the motor and the wellbore wall. BHA analysis was used to optimize the placement of a stabilizer directly on the motor for removing this intermittent contact and generating a neutral directional tendency during rotation. After the solution had been implemented, the motor no longer saw excessive vibration levels, no signs of wear after drilling the well existed, and the sliding time was reduced greatly by reducing the building tendency of the motor in rotation.
  • A new data-visualization approach revealed an unusual data trend verified to be the result of bit-induced BHA resonance. In reviewing the data for a 5-in. motor run in the Delaware basin, a noticeable trend in the lateral vibration data was prevalent. The vibrations were observed to peak whenever the BHA was rotated at 70 rev/min. Vibration analysis revealed that this coincided with a resonance of the BHA caused by bit excitation (bit whirl). In this case, the vibrations were not detrimental to the BHA, but the scenario illustrated that resonance was present and observable.

A Framework for Automated Analysis

On the basis of the effectiveness of the model in representing the behavior of the BHA downhole, potential exists for its use as a tool for real-time vibration mitigation. This could be achieved by providing simple plots to personnel on the rig that capture critical BHA rotation speeds (anticipated BHA resonance caused by rotating the inherent mass eccentricities along the BHA), critical bit speeds (BHA resonance caused by bit whirl), and critical flow rates (BHA resonance caused by inherent whirling of the rotor within the motor) that should be avoided. Fig. 1 shows what these Critical Speed Roadmaps would look like for a rotary-­steerable-system (RSS) BHA on a hypothetical virtual rig-floor display. Here, the calculated critical speeds (RSS rev/min, bit rev/min, and flow rate) are plotted as red lines and the actual operating parameters are plotted as large circular dots. Note that, for RSS BHAs, the bit speed and RSS speed will be the same thing physically; the difference, in terms of plotting and labeling, stems from the assumed source of excitation used to calculate each one (Critical Rev/min vs. Critical Bit Speed). These plots are calculated automatically for a given BHA configuration over a specified weight-on-bit (WOB) range and can be updated readily in approximately 5 minutes; all that is needed to refresh the plots is an updated survey.

Fig. 1—Example of a Critical Speed Roadmap on a hypothetical virtual rig display.


The plots shown in Fig. 1 differ significantly from what others have termed “vibration roadmaps” in that these do not simply display lateral natural frequencies of the BHA as a function of measured depth. The lateral natural frequencies are dependent not only on the applied WOB but also on the curvature of the wellbore, neither of which are necessarily constant over the course of the wellbore. Thus, attempting to plot the lateral natural frequencies as only a function of measured depth can be misleading if this fact is not understood.

In practice, this type of display would be integrated into an automated work flow such that the Critical Speed Roadmaps are updated automatically after each survey is taken.

  1. Starting with the initial input data, a Critical Speed Roadmap would be generated for the most-recent survey depth.
  2. The rig can then drill ahead using the Critical Speed Roadmap as a guide, attempting to avoid any resonant operating parameters.
  3. Once a new survey has been taken, the Critical Speed Roadmap is recalculated; the driller then uses the new Roadmap as the drilling-parameter guideline.

Automation of Step 2 is an intriguing concept and, in the author’s opinion, one worth pursuing. While the proposed model has been shown to reasonably be accurate and reliable, this does not change the fact that errors do still exist between measured and calculated resonant frequencies of the BHA. Not only that, but it is certainly possible that a calculated resonant speed or flow rate, while present downhole, may not generate a damaging vibration response in the BHA. For this reason, an automated driller would be tremendously beneficial if it used the Critical Speed Roadmap as a guideline for determining the parameters to approach with caution.

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 191780-18ERM-MS, “Field Validation of a New BHA Model and Practical Case Studies in Unconventional Shale Plays, With a Framework for Automated Analysis for Operations Support,” by J.K. Wilson, Scientific Drilling International, prepared for the 2018 SPE/AAPG Eastern Regional Meeting, Pittsburgh, Pennsylvania, USA, 7–11 October. The paper has not been peer reviewed.

BHA Behavior-Prediction Model Offers Potential for Automated Analysis

01 December 2019

Volume: 71 | Issue: 12

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