This paper is devoted to the homogenization of a nonlinear one-dimensional problem as a particular case of laminated composite and its solution by a Wavelet-Galerkin method. This approach is an extension of this method to nonlinear problems. Theoretical results are given and numerical examples are presented.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractDuring the last years, several efforts have been done focused on developing the automatic computer-aided well test analysis.Traditionally, conventional gradient-based algorithms such as Levenberg-Marquardt have been used for parameters estimations. However, recently the use of new approaches based on global optimization methods has been introduced in the literature, mainly attempting to eliminate the influence of the initial guess on the overall regression, and overcoming the uniqueness problems.The aim of this work is to study the characterization of naturally fractured vuggy reservoirs via the automatic well test analysis by using a triple porosity model recently developed. Thus, an Evolutionary Algorithm (EA) was designed, taking into account the important fact that the triple porosity case may yield multiple solutions. Therefore, several aspects such as the parameters estimations with high precision and the necessity of developing analysis techniques computationally efficient are taken into account in the design of algorithms.According to the above, it is demonstrated that the algorithm developed in this work allows finding the multiple optimal solutions, with the desired precision. Advantages of the EA over the classical Levenberg-Marquardt method for this specific well test analysis problem are also discussed.

Geosciences Numerical Methods Modélisation numérique en géosciencesOil & Gas Science and Technology -Rev. IFP Energies nouvelles, Vol. 69 (2014), No. 4, Copyright © 2014, IFP Energies nouvelles > EditorialJ. E. Roberts > Modeling Fractures in a Poro-Elastic MediumUn modèle de fracture dans un milieu poro-élastique > Modeling Fluid Flow in Faulted BasinsModélisation des transferts fluides dans les bassins faillés Re´sume´-Analyse des puits d'essai de re´servoirs vacuolaires naturellement fracture´s avec un mode`le de triple porosite´-double perme´abilite´et une me´thode d'optimisation globale -L'objectif de ce travail est l'e´tude de la caracte´risation automatique de re´servoirs de pe´trole fracture´s ve´siculaires via l'analyse des puits d'essai, avec un mode`le de triple porosite´et de perme´abilite´double. Les parame`tres qui doivent eˆtre identifie´s comme ceux du mode`le, sont l'e´coulement entre les trois media, les ratios de stockage, la porosite´, le ratio de perme´abilite´, l'effet de stockage, la perme´abilite´de peau et totale. Dans ce travail, nous avons effectueĺ 'interpre´tation de l'essai dans l'espace de Laplace, en utilisant des algorithmes nume´riques pour transfe´rer les donne´es obtenues dans un espace de temps complet en un espace de Laplace. Le proble`me de l'interpre´tation des tests dans l'espace de Laplace est pose´comme un proble`me d'optimisation des moindres carre´s non line´aires avec boıˆte contrainte et ine´galite´line´aire contrainte, ce qui est ge´ne´ralement re´solu en utilisant des me´thodes de type Newton avec une re´gion de confiance. Cependant, les me´thodes locales comme celle utilise´e dans notre travail appele´e TRON, ou la me´thode bien connue de Levenberg-Marquardt, ne sont pas souvent en mesure de trouver une solution optimale avec un bon ajustement des donne´es. É galement la caracte´risation automatique des re´servoirs du pe´trole fracture´s vacuolaires via l'analyse des puits d'essai avec le mode`le de porosite´-perme´abilite´a`double triple, peut, comme la plupart des proble`mes inverses, donner des solutions multiples avec une bonne corre´lation des donne´es. Pour faire face a`ces spe´cificite´s, nous avons utilise´une approche avec la me´thode d'optimisation globale appele´e Tunneling Method (TM). Dans l'adaptation de l'algorithme, nous prenons en compte des proble`mes comme le fait que le l'estimation des parame`tres doit eˆtre formule´e avec une grande pre´cision, comme la pre´sence de bruit dans les mesures et comme la ne´cessite´de re´soudre le proble`me de calcul rapidement. Nous de´montrons dans cette e´tude que l'utilisation de TM est une alternative efficace et robuste pour re´soudre la caracte´risation des puits d'essai, du fait que plusieurs solutions avec un bon ajustement aux donne´es aient e´te´obtenues.Oil & Gas Science and Technology -Rev. IFP Energies nouvelles, Vol. 69 (2014), No. 4, pp. 653-671 Copyright Ó 2014, IFP Energies nouvelles DOI: 10.2516 Abstract -Well Test Analysis of Naturally Fractured Vuggy Reservoirs with an Analytical Triple P...

This paper presents the advances on the characterization of Naturally Fractured Vuggy Reservoirs (NFVR) located in the South East Gulf of Mexico. Halos, fractures and vugs were characterized through well tests using the triple porosity–double permeability (3φ-2k) model. Through the analysis of well and imagelogs was determined the predominance of high vuggyporosity producing intervals, so that the pressure data were analyzed using a triple porosity-double permeability (3φ -2k) approach, with total and partial penetration. These NFVRs have vuggy and fracture porosity, with triple porosity, matrix, fractures, and vugs, or matrix, vugs with their halos. In both cases, the 3φ-2k model is appropriate to characterize these fields. These models, recently presented involve the determination of 9 and 13 parameters, for total and partial penetration, respectively, which implies challenges in terms of the uniqueness of the results. In this way, it is suggested to consider information from other sources like cores, well logs, and image logs, in order to select characteristic values for some of the parameters of the model of interpretation, specifically the storage ratios for vugs and fractures, ωv and ωf, and in this way to eliminate the non-uniqueness problem. Thus, the integration of static and dynamic information is a key element for a complete description of NFVR. The 3φ-2k model allows better data fits than the classical dual-porosity model, obtaining more information related to the interactions of the three different media. The sum of vuggy and fracture porosity obtained from 3φ-2k model is not equal to the secondary porosity obtained from the dual-porosity model. If partial penetration effects are present, it is recommended to perform the analysis taking into account these effects because information on the vertical communication of vugs and fractures can be obtained with the 3φ-2k model. It is confirmed through the analysis of well-tests with partial penetration that the vertical communication of vugs can be more important than the horizontal communication. It is crucial to obtain fracture and vug connectivity in both horizontal and vertical direction, mainly because these reservoirs are sharing a common aquifer. The objective of this work is to demonstrate the application of a 3φ-2k model to determine several parameters related to reserves and productivity of NFVR. Vertical connectivity of both vugs and fractures are important parameters when an aquifer is underlying heavy oil NFVR, because these areas could establish preferential routes for the advancement of water.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractDuring the last years, several efforts have been done focused on developing the automatic computer-aided well test analysis.Traditionally, conventional gradient-based algorithms such as Levenberg-Marquardt have been used for parameters estimations. However, recently the use of new approaches based on global optimization methods has been introduced in the literature, mainly attempting to eliminate the influence of the initial guess on the overall regression, and overcoming the uniqueness problems.The aim of this work is to study the characterization of naturally fractured vuggy reservoirs via the automatic well test analysis by using a triple porosity model recently developed. Thus, an Evolutionary Algorithm (EA) was designed, taking into account the important fact that the triple porosity case may yield multiple solutions. Therefore, several aspects such as the parameters estimations with high precision and the necessity of developing analysis techniques computationally efficient are taken into account in the design of algorithms.According to the above, it is demonstrated that the algorithm developed in this work allows finding the multiple optimal solutions, with the desired precision. Advantages of the EA over the classical Levenberg-Marquardt method for this specific well test analysis problem are also discussed.