Probabilistic Drilling-Optimization Index Guides Drillers To Improve Performance

This paper proposes a metric for quantifying drilling efficiency and drilling optimization that is computed by use of a Bayesian network.


This paper proposes a metric for quantifying drilling efficiency and drilling optimization that is computed by use of a Bayesian network. The network combines the identification of drilling dysfunctions (i.e., vibrational modes), autodriller dysfunctions, and mechanical-specific-energy (MSE) tracking into a single, normalized quantity that the driller can use to help decide which control parameters to adjust. The driller may be provided with operational cones on a weight-on-bit (WOB)/rotary speed plot to assist in this task.


The method proposed in this paper combines real-time surface measurements available on a drilling rig, derived quantities such as MSE and bit aggressiveness, and formation data (e.g., rock strength) into a probabilistic framework capable of handling the inherent uncertainty in the data and the process. The measured and derived parameters are encoded into a set of probabilistic features indicative of either the location of a particular physical attribute or a trend/movement of the attribute. These features are used to infer the beliefs of various drilling dysfunctions as well as the belief of an optimal drilling condition. The end result is a drilling-optimization index calculated whenever a drilling activity occurs. Because of its holistic nature, this index factors in the presence of various dysfunctions as well as suboptimal drilling rates. Additional dysfunctions can be added to the index easily, and the Bayesian network is forgiving when some data is missing. The index can be integrated easily into a decision-support system for monitoring drilling performance and providing recommendations for improved efficiency. Fig. 1 shows a detailed flowchart of the method.

Fig. 1—Flow chart for drilling-optimization-index calculation.

Processing of Real-Time Drilling Inputs

The method starts by reading real-time drilling parameters, such as surface torque, rotary speed, WOB, rate of penetration (ROP), differential pressure, and control set points. If different rig sensors report data at different frequencies, a time synchronization of the sensor measurements is performed to depict the trends of the data collected by the various sensors accurately as a function of time. Next, preprocessing of the data collected from the sensors is performed. Preprocessing steps include removing obvious data outliers, as well as null or missing values, and summarizing high-frequency data to one or a few data points.

The next step involves identifying the rig activity. If the rig activity is drilling (either rotating or sliding), the system proceeds to calculate the MSE, bit aggressiveness, and stick/slip-alarm magnitude using the collected sensor readings.

Feature Extraction for Detecting Drilling Dysfunction

Once the measured and derived drilling parameters are obtained, their instantaneous values and trends are converted into location and movement features. Each feature outputs a probability value. For example, a probability may be determined for the location of an attribute value on a threshold range, from a low threshold to a high threshold.

Movement features may be classified using linear curve fitting performed over a moving window of attribute values. A probability function for the attribute of interest having an increasing, decreasing, or constant trend is determined by comparing the coefficient related to the slope of the linear fit with a negative or positive fit threshold. Movement features also may be analyzed by determining if a feature is erratic by looking at the standard deviation of measurements over a moving window. Derived drilling parameters such as MSE and bit aggressiveness may have highly erratic trends that indicate the presence of bit bounce or stick/slip. By combining the probability of a feature being erratic with its mean trends (increasing, decreasing, or constant), differentiation of specific dysfunctions can be further enhanced. If unconfined-compressive-strength (UCS) data is available, the UCS variation over depth may be compared with the MSE trends as an additional feature to distinguish between dysfunctions and normal trends resulting from formation changes.

Bayesian Modeling of Drilling Dysfunctions

The location and movement features are aggregated into a Bayesian network representing the drilling process. A set of discrete probabilistic weights, or conditional probability tables, connects the various nodes in the Bayesian network model. The drilling-dysfunction node is assigned a prior probability distribution on the basis of the expected frequency of occurrence for each of the modeled dysfunctions, which include bit balling, bit bounce, stick/slip, whirl, and a lumped category for other dysfunctions (e.g., topdrive failure, downhole-motor ­failure, and malfunctioning autodriller systems). The posterior probability distribution of the drilling-dysfunction node is updated whenever a drilling activity is recorded. The outcome of the drilling-dysfunction node corresponding to no dysfunction detected yields the instantaneous value of the drilling-optimization index. The probabilistic formulation naturally results in a drilling-optimization (drilling-efficiency) index between zero and unity, with unity representing optimal drilling and zero representing inefficient drilling.

Using the Drilling-Optimization Index in Real-Time Data-Aggregation Software

The drilling-optimization index has been integrated into a real-time drilling-data-aggregation and -distribution software that is currently in use on 20 onshore rigs in North America. The drilling-optimization index and drilling-dysfunction beliefs feature dedicated displays, such as the ones shown in Fig. 2. A moving average of the drilling-optimization index over a predefined period of time or depth interval is computed to filter out noise in the calculations. A dial indicator with intuitive color coding (i.e., green for optimal drilling, yellow for intermediate values, and red for inefficient drilling) allows for facile monitoring of the drilling efficiency by the driller. Human-factors-engineering principles were used in designing the displays. The drilling-optimization index also may be graphed on a depth-based chart. This information may be used to generate daily reports and to benchmark drilling parameters for various depths and geological formations. The goal of providing drilling-efficiency/-inefficiency data may be to improve driller skills, to set benchmarks for drilling in conjunction with internal knowledge, and to prevent drill-bit or mud-motor failure.

Fig. 2—Display showing drilling-efficiency index as dial indicator and time-based and depth-based trend charts. The dial indicator is color-coded to indicate regions of good, intermediate, and poor drilling efficiency.


Furthermore, the system automatically determines whether the drilling-optimization index is below a specified threshold. When the value falls below the threshold, the system provides a recommendation for improving the drilling performance. This recommendation is provided in the form of a suggested parameter change, such as increasing or decreasing the rotary speed or WOB, or a combination of these actions (for example, decreasing WOB while increasing rotary speed to avoid stick/slip). The suggestion may be presented as a text input or more visually. The figure shows operational regions for the driller to move to in response to several different dysfunctions. The cone angle, height, and reference angle are calculated on the basis of all values of dysfunction beliefs and the current operating point. A recommendation may also be made to engage or disengage an automatic control system if one is available, such as an autodriller, or a stick/slip-mitigation system.


  • An index that aggregates all the drilling dysfunctions makes it easier for the driller to find good WOB and rotary-speed operating points. The driller is thereby freed from the task of monitoring trends.
  • The optimal drilling regions on a WOB/rotary-speed plot vary quite a bit even among wells on the same pad. It is difficult (if not impossible) to arrive at such regions through models. This is because of the large uncertainty in knowing formation changes, hole geometry, tortuosity of the well, and bit condition, for example. Heat maps generated through models are likely to be flawed and simplistic.
  • The drilling-efficiency index and the dysfunction-belief values enable the driller to move toward a better solution, but global optimality is not guaranteed because of the highly nonlinear nature of the drilling dynamics.
  • Post-well analysis for drilling parameters should be performed with caution. While these drilling parameters may be good starting points, real-time data reflect reality better and can provide pointers for better drilling parameters.
  • Operational cones can be calculated and provided to the drillers to help them try out drilling parameters that attenuate dysfunctions and improve drilling efficiency.

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 186166, “A Novel Probabilistic Rig-Based Drilling-Optimization Index To Improve Drilling Performance,” by A. Ambrus, SPE, P. Ashok, SPE, A. Chintapalli, and D. Ramos, Intellicess, and M. Behounek, SPE, T.S. Thetford, SPE, and B. Nelson, SPE, Apache, prepared for the 2017 SPE Offshore Europe Conference and Exhibition, Aberdeen, 5–8 September. The paper has not been peer reviewed.