Bayesian change point prediction for downhole drilling pressures with hidden Markov models
Bibliographic record
Abstract
Abstract In the drilling of oil wells, the need to accurately detect downhole formation pressure transitions has long been established as critical for safety and economics. In this article, we examine the application of Hidden Markov Models (HMMs) to oilwell drilling processes with a focus on the real time evolution of downhole formation pressures in its partially observed state. The downhole drilling pressure system can be viewed as a nonlinear, non‐degrading stochastic process whose optimum performance is in a region in its warning state prior to random failure in time. The differential pressure system is modeled as a hidden 3 state continuous time Markov process. States 0 and 1 are not observable and represent the normally pressured (initiating ) and abnormally pressured or warning (reducing ) states respectively. State 2 is the observable failure state (from negative and loss of well control). The signal process of the evolution of differential pressure is identified in the changes in the observable rate of penetration (ROP) encoded in drilling performance data. The state and observation parameters of the HMM are estimated using the Expectation Maximization (EM) algorithm and we show, for a univariate system with a depth dependent time relationship, that the model parameter updates of the EM algorithm equation have explicit solutions. A Bayesian inference model, to determine the safety threshold of the system and early failure prediction at each sampling epoch, is thereafter proposed. The application of our stochastic model of the dynamic evolution of downhole pressures in operational time is illustrated with a hindcast case example. The analysis showed strong early indication of probable failure in real time and was validated in the field post drilling system failure that resulted in significant recovery costs. The potential to predict the differential pressure state transitions ahead of the bit represents a capability not currently available in the industry. This opens up significant opportunity for value creation from optimizing drilling operations to deliver substantial savings in well construction costs.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".