Impact of Distance-of-Investigation Calculations on Rate-Transient Analysis of Unconventional Gas and Light-Oil Reservoirs: New Formulations for Linear Flow
Bibliographic record
Abstract
Summary Long-term transient linear flow of hydraulically fractured vertical and horizontal wells completed in tight/shale gas wells has historically been analyzed by use of the square-root-of-time plot. Pseudovariables are typically used for compressible fluids to account for pressure-dependence of fluid properties. Recently, a corrected pseudotime has been introduced for this purpose, in which the average pressure in the distance of investigation (DOI) is calculated with an appropriate material-balance equation. The DOI calculation is therefore a key component in the determination of the linear-flow parameter (product of fracture half-length and square root of permeability, xfk) and the calculation of contacted fluid in place. Until now, the DOI for transient linear flow has been determined empirically, and may not be accurate for all combinations of fluid properties and operating conditions. In this work, we have derived the DOI equations analytically for transient linear flow under constant-flowing-pressure and -rate conditions. For the first time, rigorous methodologies have been used for this purpose. Two different approaches were used: the maximum rate of pressure response (impulse concept) and the transient/boundary-dominated flow intersection method. The two approaches resulted in constants in the DOI equation that are much different from previously derived versions for the constant-flowing-pressure case. The accuracy of the new equations was tested by analyzing synthetic production data from a series of fine-grid numerical simulations. Single-phase oil and gas cases were analyzed; pseudovariable alteration for pressure-dependent porosity and permeability was required in the analysis. The calculated linear-flow parameters, determined from our new DOI formulations for the constant-flowing-bottomhole-pressure (FBHP) case, and the input values to numerical simulation, are in good agreement. Of the two new DOI-calculation methods provided, the maximum rate of pressure response (unit impulse method) provides more accurate results. Finally, a field case was analyzed to determine the impact of DOI formulations on derivations of the linear-flow parameter from field data. Linear-flow analysis on the basis of the DOI calculations presented in this work is significantly improved over previous formulations for constant FBHP.
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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 | 0.004 | 0.002 |
| 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".