Use of the Fourier-Laplace transform and of diagrammatical methods to interpret pumping tests in heterogeneous reservoirs

Nœtinger, B.; Gautier, Yann

doi:10.1016/s0309-1708(97)00014-6

Cited by 23 publications

(20 citation statements)

References 10 publications

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“…A different approach to the problem of computing T eff in convergent flow conditions was employed by Noetinger and Gautier [1998]. They analyzed transient converging flow using a perturbations expansion combined with the diagrammatic method in order to sum up the successive terms.…”

Section: Convergent Flowmentioning

confidence: 99%

Representative hydraulic conductivities in saturated groundwater flow

Sánchez-Vila

Guadagnini

Carrera

2006

Reviews of Geophysics

275

209

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Heterogeneity is the single most salient feature of hydrogeology. An enormous amount of work has been devoted during the last 30 years to addressing this issue. Our objective is to synthesize and to offer a critical appraisal of results related to the problem of finding representative hydraulic conductivities. By representative hydraulic conductivity we mean a parameter controlling the average behavior of groundwater flow within an aquifer at a given scale. Three related concepts are defined: effective hydraulic conductivity, which relates the ensemble averages of flux and head gradient; equivalent conductivity, which relates the spatial averages of flux and head gradient within a given volume of an aquifer; and interpreted conductivity, which is the one derived from interpretation of field data. Most theoretical results are related to effective conductivity, and their application to real world scenarios relies on ergodic assumptions. Fortunately, a number of results are available suggesting that conventional hydraulic test interpretations yield (interpreted) hydraulic conductivity values that can be closely linked to equivalent and/or effective hydraulic conductivities. Complex spatial distributions of geologic hydrofacies and flow conditions have a strong impact upon the existence and the actual values of representative parameters. Therefore it is not surprising that a large body of literature provides particular solutions for simplified boundary conditions and geological settings, which are, nevertheless, useful for many practical applications. Still, frequent observations of scale effects imply that efforts should be directed at characterizing well-connected stochastic random fields and at evaluating the corresponding representative hydraulic conductivities

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Section: Convergent Flowmentioning

confidence: 99%

Representative hydraulic conductivities in saturated groundwater flow

Sánchez-Vila

Guadagnini

Carrera

2006

Reviews of Geophysics

275

209

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“…For large t, there are a number N(t) ≈ π R(t) 2 / l c 2 = 2D t / l c 2 of independant permeability units in this disk. Central limit theorem shows thus that the variance of k(t) will vary like 1/N(t) ≈ 1/t: this corresponds to the prediction of the detailed calculation of Noetinger and Gautier (1998). We also understand how the measurement support size may influence the determination of permeability distributions.…”

Section: About Pressure Transients: the Self Averaging Propertymentioning

confidence: 55%

“…This linear equation has the structure of an integro differential equation, and was derived independently by Indelman (1996), and Noetinger and Gautier (1998) who used a Feynman graph approach. The memory kernel Σ(r, t) (a second order symmetric tensor) depends explicitly only on the correlation functions of the permeability of arbitrary order.…”

Section: About Pressure Transients: the Self Averaging Propertymentioning

confidence: 99%

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Multiscale Description and Upscaling of Fluid Flow in Subsurface Reservoirs

Nœtinger

Zargar

2004

Oil & Gas Science and Technology - Rev. IFP

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Résumé -Description multiéchelle des écoulements dans les réservoirs souterrains -Les formations géologiques sont des objets naturels complexes, sièges d'innombrables processus géologiques, mécaniques, physico-chimiques se déroulant sur des échelles d'espace et de temps extrêmement larges. Ainsi, des propriétés de mouillabilité directement issues de phénomènes moléculaires influencent directement les déplacements eau-huile, et donc évidemment la récupération finale du pétrole. De même, les hétérogénéités du réservoir, couplées aux non-linéarités de la mécanique des fluides, jouent un rôle essentiel pour localiser les écoulements dans des chenaux préférentiels. De façon à gérer cette complexité, et à hiérarchiser au mieux l'influence des nombreux phénomènes et paramètres, il est essentiel de disposer d'une description multiéchelle du transport de fluides dans ces milieux. Ceci permet aux ingénieurs en géosciences de travailler un modèle de terre partagé, réceptacle du savoir géologique, géophysique, ainsi que des données de gisement permettant l'intégration des divers métiers. On peut ainsi se concentrer sur les principaux phénomènes contrôlant l'écoulement de l'huile, et donc, sa récupération. Ceci aide les ingénieurs à intégrer les données issues de mesures de natures diverses à des échelles différentes et à diminuer les incertitudes, permettant ainsi la prise de meilleures décisions économiques. Dans cet article, nous présentons la philosophie globale des techniques de changement d'échelle, en y incluant la description des concepts les plus récents d'approches multiéchelles. Abstract -Multiscale Description and Upscaling of Fluid Flow in Subsurface Reservoirs In order to face this complexity, and to be able to hierarchize the influence of the various relevant geological and physico-chemical phenomena, it is thus essential to handle a multiscale description of fluid transport in these reservoirs. This is an essential tool to help reservoir engineers to focus on the crucial phenomena that control the flow. This helps them to integrate data, and this results in a lowering of the uncertainties of the reservoir description that enhances economical decisions. In this paper, we present classical upscaling approaches, as well as more recent multiscale concepts. Upscaling of Fluid Flow in Oil ReservoirsMise à l'échelle des écoulements dans des réservoirs pétroliers D o s s i e rOil & Gas Science and Technology -Rev. IFP, Vol. 59 (2004)

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“…We use the transfer function for the dualporosity inner region of the tri-linear model (Ozkan et al, 2009) to obtain the results discussed in the next section. An alternative procedure is given in Noetinger and Gautier (1998) and Noetinger et al (2001). Their work also includes discretization of the developed fluid flow equation and the CTRW algorithm over the porous medium.…”

Section: Figurementioning

confidence: 99%

Modeling of 1D Anomalous Diffusion in Fractured Nanoporous Media

Albinali¹,

Holy²,

Sarak³

et al. 2016

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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-Fractured nanoporous reservoirs include multi-scale and discontinuous fractures coupled with a complex nanoporous matrix. Such systems cannot be described by the conventional dual-porosity (or multi-porosity) idealizations due to the presence of different flow mechanisms at multiple scales. More detailed modeling approaches, such as Discrete Fracture Network (DFN) models, similarly suffer from the extensive data requirements dictated by the intricacy of the flow scales, which eventually deter the utility of these models. This paper discusses the utility and construction of 1D analytical and numerical anomalous diffusion models for heterogeneous, nanoporous media, which is commonly encountered in oil and gas production from tight, unconventional reservoirs with fractured horizontal wells. A fractional form of Darcy's law, which incorporates the non-local and hereditary nature of flow, is coupled with the classical mass conservation equation to derive a fractional diffusion equation in space and time. Results show excellent agreement with established solutions under asymptotic conditions and are consistent with the physical intuitions.Résumé -Modélisation de la diffusion anormale en 1D dans des milieux nanoporeux fracturés -Des réservoirs nanoporeux fracturés comprennent des fractures à échelles multiples et discontinues couplées à une matrice nanoporeuse complexe. Ces systèmes ne peuvent pas être décrits par les modélisations conventionnelles à double porosité (ou multi-porosité) du fait de la présence de différents mécanismes de flux à multiples échelles. Des approches de modélisation plus détaillées, telles que les modèles de Réseau de Fracture Discret (DFN, Discrete Fracture Network) souffrent de même des exigences extensives en matière de données, dictées par la complexité des échelles de flux, qui nuisent éventuellement à l'utilité de ces modèles. Le présent article traite de l'utilité et de la construction de modèles analytiques et numériques de diffusion anormaux en 1D pour des milieux hétérogènes nanoporeux, qui se rencontrent communément dans la production de pétrole et de gaz, pour les réservoirs étanches, non conventionnels avec des puits horizontaux fracturés. Une forme fractionnée de la loi de Darcy, qui comprend la nature non-locale et héréditaire du flux, est reliée à l'équation de conservation de la masse classique afin d'obtenir une équation de diffusion fractionnée dans l'espace et le temps. Les résultats montrent une parfaite concordance avec des solutions établies dans des conditions asymptotiques et ils sont conformes aux intuitions physiques.

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Use of the Fourier-Laplace transform and of diagrammatical methods to interpret pumping tests in heterogeneous reservoirs

Cited by 23 publications

References 10 publications

Representative hydraulic conductivities in saturated groundwater flow

Representative hydraulic conductivities in saturated groundwater flow

Multiscale Description and Upscaling of Fluid Flow in Subsurface Reservoirs

Modeling of 1D Anomalous Diffusion in Fractured Nanoporous Media

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