The research team, led by Zhanpeng Liu and Wensheng Xiao, combined failure mode and effects analysis, Bayesian networks, risk matrices, and fuzzy comprehensive evaluation into one integrated method. Each technique has well-known strengths and blind spots. FMEA can systematically identify potential failure modes but is highly subjective. Bayesian networks excel at quantitative forward and backward inference yet cannot judge how severe a failure’s consequences would be. Risk matrices offer a visual representation of occurrence and severity but cannot assess the risk level of the system as a whole. Fuzzy comprehensive evaluation handles vague, uncertain information but again depends on subjective judgment. By weaving these approaches together, the researchers aimed to let each method compensate for the weaknesses of the others, producing a single assessment that yields both the system failure probability and the risk level of every individual failure mode.

The workflow begins with a fault tree analysis of the motor, in which twenty bottom-event failure modes across six components, the rotor, bearings, windings, permanent magnets, controller, and mechanical seal, are mapped into a Bayesian network. Prior probabilities are derived from historical failure rates in the OREDA offshore reliability database, adjusted upward by expert judgment to reflect the brutal conditions of underground drilling. Bayesian forward inference then computes the overall system failure probability, while backward diagnostic inference produces posterior probabilities revealing which failure modes are most likely responsible when the system fails. In the baseline assessment, the system failure probability came out at 0.428, a strikingly high figure that underscores how punishing the drilling environment is for these machines.

Next comes importance analysis, a mathematical step that quantifies how much each failure mode contributes to system failure. The team calculated three indices: probabilistic importance, which measures the impact of a component’s failure probability on system failure; structural importance, which reflects a component’s position in the system architecture; and critical importance, which combines both failure probability and sensitivity. Because all twenty failure modes feed the system through identical OR-gate logic, their structural importance is equal, but their probabilistic and critical importance diverge dramatically. Rotor breakage, for instance, posted a probabilistic importance of 1.3782, far above its peers, while bearing wear registered a posterior probability of 0.612, the highest of any mode, simply because bearings grind against each other every moment the motor spins.

These quantitative outputs then feed the qualitative side of the framework. The posterior probability of each failure mode determines its occurrence rating on a five-level scale, from improbable to frequent, while the critical importance determines its severity rating, from negligible to catastrophic. The two ratings fuse into a composite risk index called ROS, weighted 0.4 toward occurrence and 0.6 toward severity, a deliberate choice reflecting the safety-critical nature of drilling, where even rare events with devastating consequences demand priority attention. The resulting ROS values map onto a fuzzy evaluation matrix through a parabolic membership function, and the weights of that matrix come directly from the importance analysis rather than from pure expert opinion, reducing the subjectivity that plagues conventional assessments.

The baseline results identified winding phase-to-phase short circuit as the single highest-risk failure mode, with a ROS value of 4.2 placing it firmly in the high-risk category. Rotor dynamic eccentricity and permanent magnet partial demagnetization followed at 3.6 each, classed as medium-high risk. Perhaps more revealing were the failure modes with severe consequences but vanishingly low occurrence, including rotor breakage, bearing breakage, and permanent magnet breakage, all rated medium risk despite being improbable. The framework’s dual weighting captured exactly the kind of nuance that pure probability-based methods miss: a rare failure that destroys the motor deserves as much managerial attention as a common one that merely degrades performance. The fuzzy evaluation concluded that the system sat at medium risk with a membership probability of 0.498, but with a worrying 0.351 probability of medium-high risk.

Armed with this diagnosis, the researchers proposed targeted countermeasures for every failure mode, ranging from corona-resistant enameled wire and vacuum pressure impregnation for the windings to hastelloy springs and fluorocarbon or EPDM elastomers for the seals, matched to oil-based and water-based mud chemistries respectively. For winding faults, they applied weak magnetic current injection, multi-phase redundancy, and winding redundancy, allowing the motor to shed faulty phases gracefully while maintaining partial power. After implementing the improvements, the system failure probability dropped from 0.428 to 0.394, the mean time between failures rose from 1,847 to 2,032 hours, and the medium-high risk membership probability fell from 0.351 to 0.245. The highest-risk failure mode, the winding short circuit, saw its ROS value plunge from 4.2 to 3.2, a 23.8 percent risk reduction.

What distinguishes this study from earlier hybrid approaches is its unusually rigorous treatment of uncertainty and validation. The team ran a Monte Carlo simulation with 10,000 samples, assuming failure rates follow log-normal distributions with a 20 percent coefficient of variation, and found that the 95 percent confidence intervals of key outputs remained narrow, less than 15 percent of their mean values. A perturbation analysis of the weighting coefficients showed that risk rankings stay stable, with Spearman rank correlations above 0.88, as long as severity retains reasonable dominance, confirming the wisdom of the 0.4-0.6 split. The importance-based weights were cross-checked against the entropy weight method and the CRITIC method, with Kendall’s coefficient of concordance reaching 0.82, indicating strong agreement between expert judgment and data-driven weighting. A paired bootstrap test and a Wilcoxon signed-rank test both confirmed that the post-improvement risk reduction was statistically significant, with p below 0.001.

The authors also introduced three methodological innovations that broaden the framework’s reach. A risk coupling coefficient quantifies how strongly each failure mode couples with environmental loads such as vibration, high temperature, current fluctuations, and high-pressure drilling fluid, distilled from a multi-factor coupling matrix that identified twenty high-probability coupled failure modes. An adaptive risk transfer function models nonlinear propagation from component-level risk to system-level risk, capturing synergistic effects that simple OR-gate logic overlooks. And a risk entropy metric measures how dispersed or concentrated the system’s risk profile is; it fell from 1.42 before improvement to 1.24 after, signaling reduced uncertainty in the risk landscape.

The framework is not without limitations, which the authors acknowledge candidly. Integrating four methodologies creates a complex model with substantial computational overhead, and exact Bayesian inference scales exponentially with the number of failure modes, though hierarchical decomposition into sub-networks reduces the complexity from an intractable O(2^100) to a manageable O(10 times 2^10) for a hundred-mode system split across ten components. Prior probabilities still lean on the OREDA database and expert experience, which update infrequently, and the static Bayesian network does not yet ingest real-time sensor data. Future work, the team suggests, will move toward dynamic Bayesian networks fed by live monitoring evidence, adaptive neuro-fuzzy membership functions optimized by backpropagation, and hierarchical architectures spanning failure mode, component, subsystem, and system layers. For now, the study offers drilling engineers something genuinely valuable: a single, statistically validated assessment that tells them not just whether their motor is likely to fail, but exactly which of twenty failure modes deserves their attention first, and how much safer each repair will make it.

Subject of Research: Hybrid fuzzy risk assessment of drilling permanent magnet synchronous motors using FMEA and Bayesian networks

Article Title: An improved fuzzy risk assessment method fusing FMEA and BN for drilling permanent magnet synchronous motors

Article References: Liu, Z., Xiao, W., Cui, J., Wang, H., & Mei, L. (2026). An improved fuzzy risk assessment method fusing FMEA and BN for drilling permanent magnet synchronous motors. Results in Engineering, 32, Article 113047. https://doi.org/10.1016/j.rineng.2026.113047

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113047

Keywords: risk assessment, FMEA, Bayesian network, fuzzy comprehensive evaluation, permanent magnet synchronous motor, drilling motor, reliability engineering, risk matrix, Monte Carlo simulation, importance analysis, oil and gas drilling, failure modes

Water-based drilling fluids are the workhorses of well construction. They carry rock cuttings out of the borehole, stabilize the wellbore against collapse, control formation pressures, lubricate the drill string, and minimize damage to the productive formations encountered along the way. The performance of these fluids depends heavily on bentonite, a clay dominated by sodium montmorillonite, whose remarkable swelling capacity, thixotropic behavior, and ability to form thin, low-permeability filter cakes make it the industry’s standard viscosifying and filtration-control agent. Yet despite Nigeria’s extensive clay deposits spread across several geological formations, most local clays perform poorly compared with commercial bentonite, forcing operators to rely on imports whose prices and availability fluctuate with global supply conditions.

Previous attempts to replace imported bentonite entirely with local clays have demanded extensive chemical beneficiation or high dosages of synthetic additives to meet API specifications, strategies that introduce operational risks and drive up treatment costs. The research team, led by Lawrence Ifeanyi Igbonekwu, took a different and more pragmatic path: partial replacement. Building on an earlier study in which several beneficiation routes were tested on Nteje clay from Anambra State, the researchers selected the Na₂EDTA/NaCl sodium-saturation treatment, designated NC3, as the most effective upgrade of the raw material. The new study set out to answer an entirely different engineering question: how far can this beneficiated clay go as a bentonite extender before drilling-fluid performance begins to fail?

To find out, the team formulated mud samples at a constant total clay concentration of 22 grams per laboratory barrel, dispersing the clay blends in 350 milliliters of distilled water and mixing them with a five-spindle multimixer before allowing 24 hours of hydration. Imported bentonite was progressively substituted by NC3 in eleven formulations ranging from 0 to 100 percent replacement. All rheological and filtration measurements followed the recommended procedures of API RP 13B-1, using a Fann Model 35A rotational viscometer for dial readings at standard speeds and a Fann Model 300 low-temperature low-pressure filter press operated at 100 psi for 30 minutes. This rigorous standardization allowed the researchers to judge every blend against well-established API screening criteria.

The rheological results revealed a clear and systematic pattern. The 600 rpm viscometer reading, a key indicator of high-shear viscosity, declined steadily from 53 centipoise for the pure bentonite mud to 31 centipoise at 60 percent NC3 substitution, still above the API minimum requirement of 30 centipoise, before collapsing to just 13 centipoise in the fully local system. Plastic viscosity, which reflects internal friction from solid particles, remained in the stable range of 8 to 10 centipoise for blends containing up to 50 percent NC3, indicating that moderate substitution does not upset the mechanical structure of the fluid. Yield point, the minimum stress needed to initiate flow, fell from 33 to 13 pounds per 100 square feet over the same span, while the yield point to plastic viscosity ratio, an important measure of cuttings-carrying capacity, stayed within the recommended screening range of 0.75 to 3.0 at the 50 and 60 percent substitution levels.

Shear-thinning behavior, the hallmark of a well-designed drilling fluid, persisted across the blended formulations. The flow behavior index derived from viscometer data remained low for bentonite-rich systems, signaling strong pseudoplasticity, and rose only gradually as NC3 content increased. This matters because shear-thinning fluids suspend cuttings effectively at low shear when circulation stops, yet flow readily and impose lower frictional pressure losses at high shear during pumping. Gel strength measurements told a similar story: moderate NC3 additions produced sufficient structural buildup to hold cuttings and weighting materials in suspension without creating the punishing pump pressures that accompany circulation restarts, while NC3-rich systems showed weakened gels that raised the risk of solids settling and barite sag under static conditions.

Filtration performance proved to be another decisive screening criterion. API fluid loss climbed steadily with NC3 content, from 8 milliliters for the base mud to 14 milliliters at 60 percent substitution, remaining under the API maximum of 15 milliliters. Beyond that threshold the losses escalated rapidly, reaching 18.3 milliliters in the fully local formulation, a 22 percent breach of the specification. Filter cake thickness followed the same trajectory, staying below 2 millimeters up to the 60 percent level but ballooning to 3.2 millimeters at full replacement. Thick, permeable cakes increase the danger of differential sticking and elevate torque and drag on the drill string, so the team photographed the cakes from the recommended blends and confirmed that they were thin and compact, measuring just 1.7 and 1.9 millimeters at the 50 and 60 percent levels respectively.

Material characterization helped explain why the clays behave so differently. X-ray fluorescence showed that both materials are dominated by silica and alumina, confirming their aluminosilicate framework, with NC3 containing 61.70 percent SiO₂ and 17.80 percent Al₂O₃ compared with 59.95 and 19.20 percent for the imported bentonite. However, X-ray diffraction revealed that NC3 is dominated by quartz with calcite, cristobalite, zeolitic phases, and iron-bearing minerals, whereas the imported bentonite displayed the characteristic montmorillonite peaks that underpin its swelling and viscosifying power. Scanning electron microscopy reinforced the contrast: the foreign bentonite exhibited the layered platelet morphology that facilitates water adsorption, interlayer expansion, and viscosity development, while NC3 showed a denser, less ordered surface. The researchers also noted that pH increased with NC3 content and that only the fully local blend met the API minimum pH of 9.5, suggesting that modest alkalinity control may be needed at lower substitution levels.

The economic analysis may prove to be the study’s most persuasive element. Using a weighted-average clay cost model scaled from the laboratory barrel to estimated well-level clay consumption, the researchers calculated that the base formulation would cost about USD 10,875 per well in clay materials alone. Blending at 50 percent NC3 reduced that figure to USD 7,312, a 33 percent saving, and at 60 percent substitution the cost fell to USD 6,600, roughly 39 percent below the import-dependent baseline. Higher substitution levels promised even deeper savings, up to 65 percent, but those gains came hand in hand with fluid losses, weak gels, and near-Newtonian flow behavior that would jeopardize drilling operations. The sweet spot, the study concludes, is the 50 to 60 percent replacement range, where API-compliant rheology and filtration coexist with substantial cost reductions.

The authors are careful to frame their findings within the limits of laboratory screening under standard test conditions; high-pressure high-temperature environments and field-scale validation remain open questions. Even so, the work delivers a practical framework for turning indigenous clay resources into industrial assets: beneficiate the local material, screen it against API performance criteria in hybrid blends, and quantify the raw material economics before committing to field trials. For a developing oil-producing nation spending scarce foreign exchange on imported bentonite, the message is striking. The mud that drills the wells of tomorrow may not need to cross an ocean first; it may be sitting, quietly, in the red earth of Anambra State, waiting to be blended in the right proportion.

Subject of Research: Experimental evaluation of beneficiated Nteje clay as a partial replacement for imported bentonite in water-based drilling fluid formulations.

Article Title: Experimental screening of beneficiated Nteje clay–bentonite blends for water-based drilling fluid formulations

Article References: Igbonekwu, L. I., Nwabanne, J. T., Abonyi, M. N., & Ezechukwu, M.-J. C. (2026). Experimental screening of beneficiated Nteje clay–bentonite blends for water-based drilling fluid formulations. Discover Geoscience, 4(1), Article 370. https://doi.org/10.1007/s44288-026-00738-5

Image Credits: AI Generated

DOI: 10.1007/s44288-026-00738-5

Keywords: water-based drilling fluid, bentonite replacement, Nteje clay, rheology, filtration, drilling mud, Nigeria, clay beneficiation, shear-thinning, raw material cost analysis, API standards, oil and gas drilling