A very high order Flux Reconstruction (FR) method for the numerical simulation of 1-D compositional fluid flow model in petroleum reservoirs
Notice bibliographique
Résumé
Compositional reservoir simulation is an extremely important tool for modeling the fluid flow in complex petroleum reservoirs, as in cases where the reservoir fluid is volatile and composed of several pseudo-components with distinct characteristics, or reservoirs that require the use of enhanced oil recovery process. For these cases, simpler black-oil models are not suitable. The compositional model involves the solution of a large system of partial differential equations, that comprises the mass conservation, the Darcy’s law and the fugacity constraints. However, the high number of equations and constraints render the compositional problems extremely complex and computationally demanding solutions. To improve accuracy and reduce the high computational costs, one can use higher than first or even second-order methods to approximate the advective flux terms in the hyperbolic conservation laws that describe the multicomponent transport in the reservoir. Those very high-order schemes can replace low-order approaches, such as the First Order Upwind (FOU) method, which is traditionally used in commercial petroleum reservoir simulators (CMG, 2019; ECLIPSE, 2022), obtaining more accurate solutions with reduced computational cost. In this work, we consider a three-phase and isothermal fluid flow of water, oil and gas and assume that there is no mass transfer between the water and the hydrocarbon phases. Physical dispersion and capillary effects are neglected. To solve the system of Partial Differential Equations (PDEs), we used the classical IMPEC (Implicit Pressure Explicit Composition) approach and, to model the complex phase behavior, we used the Peng–Robinson equation of state (PR-EOS). The classical Two Point Flux Approximation (TPFA) method is used to spatially discretize the diffusion terms in the pressure equation. For the first time in literature the very high order Flux Reconstruction (FR) method is adapted for the numerical simulation of the compositional model in petroleum reservoirs. The FR method is a numerical scheme employed to discretize the hyperbolic conservation laws using general grids. To avoid spurious oscillations in the vicinity of solution discontinuities, the h-MLP (hierarchical Multi-dimensional Limiting Process) is applied in the reconstruction stage. For the time integration, we have used the third-order Runge–Kutta approach. To appraise the robustness of our formulation, we have solved some one-dimensional benchmark problems found in literature and compared the FR solution with the FOU method and with the second-order Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) method. From our results, the FR method has shown improved accuracy, efficiency and capability of detecting sharper shocks when compared to the other methods that we have considered for the numerical modeling of the compositional flow in the present paper.
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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 | 0,001 |
| Études des sciences et des technologies | 0,000 | 0,000 |
| Communication savante | 0,000 | 0,000 |
| Science ouverte | 0,000 | 0,000 |
| Intégrité de la recherche | 0,000 | 0,000 |
| 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 ».