Tiltmeter Mapping of Measured Nonsymmetric Hydraulic-Fracture Growth in a Conglomerate/Sandstone Formation Using the Implicit Level-Set Algorithm and the Extended Kalman Filter
Notice bibliographique
Résumé
Summary A novel method to map asymmetric hydraulic-fracture propagation using tiltmeter measurements is presented. Hydraulic fracturing is primarily used for oil-and-gas well stimulation, and is also applied to precondition rock before mining. The geometry of the developing fracture is often remotely monitored with tiltmeters—instruments that are able to remotely measure the fracture-induced deformations. However, conventional analysis of tiltmeter data is limited to determining the fracture orientation and volume. The objective of this work is to detect asymmetric fracture growth during a hydraulic-fracturing treatment, which will yield height-growth information for vertical fracture growth and horizontal asymmetry for lateral fracture growth or detect low preconditioning-treatment efficiency in mining. The technique proposed here uses the extended Kalman filter (EKF) to assimilate tilt data into a hydraulic-fracture model to track the geometry of the fracture front. The EKF uses the implicit level set algorithm (ILSA) as the dynamic model to locate the boundary of the fracture by solving the coupled fluid-flow/fracture-propagation equations, and uses the Okada half-space solution as the observation model (forward model) to relate the fracture geometry to the measured tilts. The 3D fracture model uses the Okada analytical expressions for the displacements and tilts caused by piecewise constant-displacement discontinuity elements to discretize the fracture area. The proposed technique is first validated by a numerical example in which synthetic tilt data are generated by assuming a confining-stress gradient to generate asymmetric fracture growth. The inversion is carried in a two-step process in which the fracture dip and dip direction are first obtained with an elliptical fracture-forward model, and then the ILSA-EKF model is used to obtain the fracture footprint by fixing the dip and dip direction to the values obtained in the first step. Finally, the ILSA-EKF scheme is used to predict the fracture width and geometry evolution from real field data, which are compared with intersection data obtained by temperature and pressure monitoring in offset boreholes. The results show that the procedure is able to satisfactorily capture fracture growth and asymmetry even though the field data contain significant noise, the tiltmeters are relatively far from the fracture, and the dynamic model contains significant “unmodeled dynamics” such as stress anisotropy, material heterogeneity, fluid leakoff into the formation, and other physical processes that have not been explicitly accounted for in the dynamic ILSA model. However, all the physical processes that affect the tilt signal are incorporated by the EKF when the tilt measurements are used to obtain the maximum likelihood estimates of the fracture widths and geometry.
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Prédiction distillée sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Apprise à partir de 10 348 étiquettes directes de Codex et de 10 348 étiquettes directes de Gemma. Le mode candidate est l'union des têtes enseignantes seuillées; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont ni des étiquettes humaines ni des étiquettes directes de modèles de pointe.
Scores Codex et Gemma par catégorie
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,001 | 0,000 |
| Méta-épidémiologie (sens strict) | 0,000 | 0,000 |
| Méta-épidémiologie (sens large) | 0,000 | 0,000 |
| Bibliométrie | 0,000 | 0,000 |
| Études des sciences et des technologies | 0,001 | 0,000 |
| Communication savante | 0,000 | 0,000 |
| Science ouverte | 0,000 | 0,000 |
| Intégrité de la recherche | 0,000 | 0,001 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,000 | 0,000 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découleClassification
machine, non validéePrédiction automatique; un appel candidat d’une seule tête enseignante, pas un consensus.
Le détail, modèle par modèle et score par score, se trouve en fin de page sous « Comment cette classification a été obtenue ».