The central problem the researchers set out to solve is one that has plagued drilling engineering for decades. The rate of penetration depends on a handful of controllable parameters, chiefly weight on bit, rotary speed, and mud flow rate, but their effects are fiercely nonlinear and entangled with rock strength, pore pressure, in-situ stresses, and the whims of lithology. Early physics-based models, such as the classic Bourgoyne and Young formulation from 1974, required extensive calibration and performed poorly in complex reservoirs; one comparative study reported coefficients of determination as low as 0.12 when such models were applied to heterogeneous formations. Machine learning has since transformed prediction accuracy, but the field has remained fragmented. Predictive models are built to win accuracy benchmarks, then optimization algorithms are bolted on separately, meaning the subtle time-dependent patterns the models capture are never actually exploited when deciding how to drill. Worse, most models operate as black boxes, offering engineers no way to understand why a particular parameter combination is recommended, which undermines trust and slows adoption at the rig site.

The new framework, developed by Shadfar Davoodi, closes these gaps with a deliberately unified design. At its heart are two long short-term memory networks, a type of recurrent neural network built to capture dependencies across sequences. One LSTM predicts the rate of penetration, the other predicts torque, and both were trained on 5,738 records compiled from three vertical wells penetrating the Asmari Formation, a carbonate sequence of limestone, dolomitic limestone, and dolomite with unconfined compressive strength values ranging from roughly 40 to well over 100 megapascals. Crucially, the same LSTM surrogate used for prediction was embedded directly into the optimization engine, a many-objective evolutionary algorithm called NSGA-III, ensuring that the recommendations the optimizer produces rest on exactly the same model that demonstrated its predictive skill. The optimizer juggles three competing goals simultaneously: maximize drilling speed, minimize torque, and minimize mechanical specific energy, the energy required to remove a unit volume of rock.

The choice of training data reflects a subtle but important insight about machine learning in the field. Well A represented efficient drilling, with penetration rates typically between 10 and 30 meters per hour, low torque, and stable hydraulics. Well B was the nightmare scenario: intensely cemented dolomite intervals with strength approaching 300 megapascals, exceptionally low rotary speeds averaging just 3.3 revolutions per minute, and torque readings averaging over 8,000 pound-feet. By training on these two extremes, the model learned both what good drilling looks like and what corrective actions dysfunctional drilling demands. Well C, representing moderate conditions, was withheld entirely as an unseen test. The results were striking: the LSTM models generalized to the unseen well with a coefficient of determination of 0.80 for penetration rate and a remarkable 0.98 for torque, strong evidence that the networks had learned genuine physical relationships rather than memorizing well-specific quirks.

Interpretability was baked into the workflow through SHAP analysis and partial dependence plots, techniques that open the black box and reveal which inputs drive predictions and in which direction. The analysis identified rotary speed as the single most influential parameter governing drilling performance, followed by standpipe pressure, which reflects hydraulic energy and hole cleaning, and weight on bit. The partial dependence curves displayed textbook drilling physics: penetration rate rises with weight on bit but saturates once an efficient operating region is reached, harder rock predictably slows the bit, and increasing drilling fluid pressure drags performance down through differential-pressure effects that hold rock chips in place. Perhaps most intriguingly, the torque model revealed an inverse relationship with rotary speed in the low-RPM regime, a signature of the transition from destructive stick-slip vibration to stable rotation, a phenomenon well known to drilling engineers but rarely recovered automatically from data.

The optimization stage enforced a hard physical constraint that many previous studies ignored: the mechanical specific energy of any recommended solution must exceed the unconfined compressive strength of the rock, the minimum energy thermodynamically required to break it. Solutions violating this rule were penalized into infeasibility, and by the twentieth generation of each optimization run more than 95 percent of candidate solutions satisfied the constraint, with final Pareto fronts containing 100 percent feasible solutions. Out-of-distribution penalties based on Mahalanobis distance kept recommendations within or near the training data envelope, guarding against the unreliable extrapolations that plague data-driven models pushed beyond their evidence. The optimizer also outperformed its rivals in head-to-head comparisons, achieving higher hypervolume and better-distributed solution sets than NSGA-II and MOEA/D under identical settings.

The predicted improvements varied dramatically between wells, and the reasons why are as instructive as the numbers themselves. Well A, already drilled near its optimum, showed only a modest 2.7 percent predicted gain in penetration rate, but the optimizer simultaneously cut torque by 5.3 percent and mechanical specific energy by 21.3 percent by shifting toward a hydraulically assisted strategy with lower rotary speed and increased flow. Wells B and C, both operated far from their ideal settings, showed predicted penetration rate improvements of 66.9 and 68.4 percent respectively, achieved by abandoning weight-dominated drilling in favor of rotation-dominated strategies. In Well B, the absolute changes were substantial: recommended weight on bit dropped from 34.5 to 11.8 kilopounds, torque fell by nearly 4,900 pound-feet, and predicted penetration rate rose from 8.4 to 14 meters per hour. Notably, the optimizer recovered established rock-mechanics principles, favoring rotary-speed-driven strategies in soft formations and balanced weight-and-speed strategies in harder rock, without ever being explicitly programmed with them.

The authors are candid about the limits of these figures. All reported improvements are surrogate-model predictions, not field-validated results, and the framework has not yet been connected to real-time data acquisition systems or tested in an actual drilling campaign. Generalization was demonstrated only by interpolation within a single carbonate field; performance in sandstones, shales, or geologically distinct reservoirs remains unproven. The study also acknowledges that standpipe pressure and drilling fluid pressure were held at measured values during optimization even though they are hydraulically coupled to flow rate, a simplification that means recommendations should be treated as indicative pending hydraulic verification. Practical deployment would also require smoothing the per-interval setpoint recommendations, since asking a drill crew to adjust parameters every ten meters is neither realistic nor necessarily safe.

Still, the architecture of the framework points clearly toward the future of the discipline. Once trained, the LSTM models deliver predictions in two to five milliseconds on a standard processor, fast enough for real-time advisory use at the rig site without retraining. The full pipeline runs offline in roughly twenty hours, generating a library of Pareto-optimal recommendations indexed by formation properties that a driller could consult as conditions change. The framework is explicitly positioned as an advisory tool rather than an autonomous control system, informing human decisions rather than replacing them. If field trials confirm the predicted gains, the implications extend well beyond a single Iranian oil field: a transparent, physics-constrained recipe for teaching machines to drill smarter could reshape the economics of one of the most capital-intensive industries on the planet, one optimized meter of rock at a time.

Subject of Research: Machine learning and multi-objective optimization of drilling performance in heterogeneous carbonate reservoirs

Article Title: Drilling performance enhancement in heterogeneous carbonate reservoirs: An integrated machine-learning and multi-objective optimization approach

Article References: Davoodi, S. (2026). Drilling performance enhancement in heterogeneous carbonate reservoirs: An integrated machine-learning and multi-objective optimization approach. Results in Engineering, 32, Article 113178. https://doi.org/10.1016/j.rineng.2026.113178

Image Credits: AI Generated

DOI: Not provided

Keywords: drilling optimization, rate of penetration, LSTM neural networks, NSGA-III, carbonate reservoirs, mechanical specific energy, SHAP interpretability, Asmari Formation, machine learning, torque prediction, multi-objective optimization, drilling engineering