PRESSURE-RATE DECONVOLUTION USING NONORTHOGONAL EXPONENTIAL FUNCTIONS DICTIONARY
Bibliographic record
Abstract
The deconvolution method, which has received considerable attention recently, is rapidly becoming one of the major tools for well test and production data analysis in the oil and gas industry. The clear justification for this approach is the fact that in well-test and production data analysis we are interested in the transient response which, for a stable linear system, is a linear combination of exponential functions. In this paper, we present a new deconvolution approach, which is potentially an important contribution to the existing body of knowledge in this field. We show that the solution of the deconvolution problem can be successfully represented as a linear combination of non-orthogonal exponential functions. In addition, we present three deconvolution algorithms. The first two algorithms are based on regularization concepts borrowed from the wellknown Tikhonov and Krylov methods. The third algorithm is based on the stochastic Monte Carlo method. Our analysis results show that the Tikhonov regularization method is stable, and feasible for a modest number of data points. Based on the results, the Krylov conjugate gradient method requires minimal storage and achieves fast convergence. This method is recommended for small to large data sets. The Monte Carlo method achieved the best results. It was able to handle large amounts of data, had minimal storage requirements, was robust to noise and avoided local minima. However, the Monte Carlo method was noticeably slower than the others. The computational results show that the exponential basis functions decomposition method provides a robust, solution in the presence of moderate levels of noise.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".