Numerical Inversion of Laplace Transforms in the Solution of Transient Flow Problems With Discontinuities
Bibliographic record
Abstract
Abstract Laplace transformation provides advantages in the solution of many pressure-transient analysis problems. Usually, these applications lead to a solution that needs to be inverted numerically to the real-time domain. The algorithm presented by Stehfest in 1970 is the most common tool in petroleum engineering for the numerical inversion of Laplace transforms. This algorithm, however, is only applicable to continuous functions and this limitation precludes its use for a wide variety of problems of practical interest. Other algorithms have also been used, but with limited success or popularity. A recent algorithm presented by Iseger in 2006 removes the restriction of continuity and provides opportunities for many practical applications. This paper exploits the useful features of the Iseger's algorithm in the inversion of continuous as well as singular and discontinuous functions that arise in the solution of pressure-transient analysis problems. The most remarkable applications are in the problems that require the use of piecewise continuous and piecewise differentiable functions, such as the use of tabulated data in the Laplace transform domain, deconvolution algorithms, and solutions that include step-rate changes as in the mini-DST tests.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".