Superposition-Rate as An Alternative to Superposition-Time
Bibliographic record
Abstract
Abstract Analysis of flow rate and pressure data, relies on the solution derived using the "constant rate" boundary condition. However, most of the time, production rates are variable. Therefore, superposition (convolution) must be used to make variable rates look like their equivalent constant rate solution. The classic way to apply the concept of superposition is to use Superposition-Time. It consists of a manipulation of time with respect to the changes in flow rates and flow durations. Valuable as that procedure is, it suffers from many pitfalls. For example, a) the resulting time is shuffled back and forth, and loses its physical significance, b) the selected superposition function makes the data tend to behave like that function (for example, radial flow superposition tends to make the data look like radial flow, while linear flow superposition tends to make the same data look like linear flow). As a result, without careful data diagnosis prior to analysis, flow regimes could be falsely interpreted, which results in misleading interpretation of well performance, and c) outliers are accentuated, resulting in a false interpretation of apparent validity. In this work, a new and innovative technique was developed using the well-known concept of superposition, but in an opposite manner. Rather than modify the time (as is done classically), we modified the rate. We derived a Superposition-Rate function which converts a variable rate situation to a constant rate equivalent. In the conventional approach to variable rate problems, we plot rate/pressure against Superposition-Time. In the approach developed in this paper, we plot Superposition-Rate directly against time (not Superposition-Time). The implementation of Superposition-Rate relies on the a priori knowledge of the flow regime. As most multi-stage hydraulically fractured horizontal wells are dominated by transient linear flow, linear Superposition-Rate was the primary focus of this paper. We developed the formulation of linear Superposition-Rate for both wells without skin and with skin. We created synthetic data sets to validate the use of Superposition-Rate. The synthetic data confirmed that Superposition-Rate successfully converts variable rate data to the equivalent constant rate solution. We also tested Superposition-Rate with real production data from shale gas reservoirs in North America. Superposition-Rate demonstrates the following advantages over Superposition-Time in production data analysis: The time scale is not modified in any way (Superposition-Time shuffles time in response to rate changes). This keeps all the data in the sequence of their occurrence, and results in a significant advantage in data-quality diagnostics.Superposition-Rate accentuates the transition from the linear flow straight line to boundary dominated flow as compared to Superposition-Time, thus aiding in the identification of flow regimes.Superposition-Rate eliminates the problem caused by Superposition-Time when outliers (i.e. abnormal production data) present. This is a significant improvement to data-quality diagnostics. With the use of Superposition-Rate outliers are not required to be removed prior to analysis.
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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 | 0.004 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".