A Comprehensive Study of <i>b</i>-Values for Proven Reserve Estimation Using Hyperbolic Decline for Vertical Commingled Gas Producers in Deep Basin Area of WCSB
Bibliographic record
Abstract
Abstract Since its discovery in the 1970's, more than 30,000 dry gas wells (over 90% of them vertical producers) have been drilled within the Deep Basin area of the Western Canada Sedimentary Basin (WCSB). Typically these wells produce from tight to medium-tight formations such as the Paddy, Cadotte, Notikewin, Falher-A, Falher-B, Falher-C, Bluesky, Cadomin and Nikanassin. The permeability of these formations ranges from about 0.001mD to 1.0mD. In an effort to maximize value, over half of the vertical wells within the Deep Basin have been commingled, producing gas from multiple formations. Every year, reservoir engineers evaluate the Proven (PDP) and/or Proven plus Probable (2P) reserves of these wells using Arps' traditional Decline Curve Analysis (DCA). In regards to hyperbolic declines, many questions frequently arise concerning the choice of b-values. Specifically, some those questions are:What b-value should be selected for wells producing from multiple formations with similar permeabilities?What b-value should be selected for wells producing from multiple formations with differing permeabilities?What is the impact on b-values if the producing layers have different pressure gradients?What is the impact on b-values if the producing layers have different drainage areas?What is the impact on b-values if the producing layers are completed differently? In the early 90's, Fetkovich had conducted an extensive study on b-values for conventional reservoirs to answer the aforementioned questions. In his study, however, the reservoir permeability that was investigated ranged from 1mD to 1000mD. This paper will discuss a comprehensive study extending Fetkovich's work to much tighter reservoirs with permeability ranging from 0.001mD to 0.1mD. This study has been conducted by simulating the annual reserve review process (using hyperbolic declines to match synthetic data from a commercial reservoir simulator) and has been further validated through practical well examples. Most importantly, a new formula has been developed to derive b-values for hyperbolic declines. This formula is especially applicable to tight gas reservoirs and will assist in answering the aforementioned questions.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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".