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Combining stochastic facies and fractal models for representing natural heterogeneity

Content Provider	Springer Nature Link
Author	Lu, Silong Molz, Fred J. Fogg, Graham E. Castle, James W.
Copyright Year	2002
Abstract	Sedimentary deposits are often characterized by various distinct facies, with facies structure relating to the depositional and post-depositional environments. Permeability (k) varies within each facies, and mean values in one facies may be several orders of magnitude larger or smaller than those in another facies. Empirical probability density functions (PDFs) of log(k) increments from multi-facies structures often exhibit properties well modeled by the Levy PDF, which appears unrealistic physically. It is probable that the statistical properties of log(k) variations within a facies are very different from those between facies. Thus, it may not make sense to perform a single statistical analysis on permeability values taken from a mix of distinct facies. As an alternative, we employed an indicator simulation approach to generate large-scale facies distributions, and a mono-fractal model, fractional Brownian motion (fBm), to generate the log(k) increments within facies. Analyses show that the simulated log(k) distributions for the entire multi-facies domain produce apparent non-Gaussian log(k) increment distributions similar to those observed in field measurements. An important implication is that Levy-like behavior is not real in a statistical sense and that rigorous statistical measures of the log(k) increments will have to be extracted from within each individual facies.Les dépôts sédimentaires sont souvent caractérisés par des faciès variés, avec une structure de faciès associée aux environnements de sédimentation et post-sédimentaires. La perméabilité (k) varie dans chaque faciès et la valeur moyenne d'un faciès peut être de plusieurs ordres de grandeur supérieure ou inférieure à celle d'un autre faciès. Des fonctions empiriques de densité de probabilité (FDP) des incréments log(k) de structures multi-faciès présentent souvent des propriétés bien modélisées par la FDP de Lévy, qui apparaît physiquement non réaliste. Il est probable que les propriétés des variations de log(k) dans un même faciès sont très différentes de celles entre les faciès. Ainsi, cela n'a pas de sens de réaliser une analyse statistique des valeurs de perméabilité provenant d'un mélange de faciès distincts. Nous avons utilisé, comme alternative, une approche d'indicateur de simulation pour générer des distributions de faciès à grande échelle, et un modèle mono-fractal, le mouvement brownien fractionnaire (mBf), pour générer des incréments log(k) à l'intérieur des faciès. Les analyses montrent que les distributions simulées de log(k) pour l'ensemble du domaine multi-faciès produit des distributions apparentes non gaussiennes des incréments log(k) semblables à celles observées dans les mesures de terrain. Une implication importante est que ce comportement semblable à celui de Lévy n'est pas réel au sens statistique et que des mesures statistiques rigoureuses des incréments log(k) devront être extraites de chacun des faciès individuels.Los depósitos sedimentarios se caracterizan a menudo por varias facies distintas, cuya estructura está relacionada con ambientes deposicionales y post-deposicionales. La permeabilidad (k) varía dentro de cada facies, y los valores medios en una de ellas pueden ser órdenes de magnitud superiores o inferiores que los correspondientes a otra. En estructuras multi-facies, las funciones de densidad de probabilidad (FDP) empíricas de los incrementos del logaritmo de la permeabilidad, log(k), exhiben a menudo propiedades que pueden ser modeladas mediante la FDP de Levy, la cual carece de un significado físico evidente. Es probable que las propiedades estadísticas de las variaciones del log(k) dentro de una misma facies sean muy diferentes a las existentes entre facies. Así, puede no tener sentido efectuar un análisis estadístico sencillo de los valores de permeabilidad obtenidos a partir de una mezcla de facies diferentes. Como alternativa, se ha utilizado un enfoque de simulación indicadora para generar distribuciones de facies a gran escala, y el modelo mono-fractal del movimiento fraccional Browniano (mfB) para generar los incrementos de log(k) dentro de las facies. Los análisis indican que las distribuciones simuladas de log(k) para todo el dominio multi-facies producen distribuciones de los incrementos de log(k) aparentemente no Gaussianas, de forma análoga a lo que se observa en medidas de campo. Una implicación importante es que el comportamiento tipo-Levy no es real en el sentido estadístico y que hay que efectuar medidas estadísticas rigurosas de los incrementos de log(k) dentro de cada facies.
Starting Page	475
Ending Page	482
Page Count	8
File Format	PDF
ISSN	14312174
Journal	Hydrogeology Journal
Volume Number	10
Issue Number	4
e-ISSN	14350157
Language	English
Publisher	Springer-Verlag
Publisher Date	2002-06-19
Publisher Institution	International Association of Hydrogeologists
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Hydrogeology Hydrology/Water Resources Geology Waste Water Technology Water Pollution Control Water Management Aquatic Pollution
Content Type	Text
Resource Type	Article
Subject	Earth and Planetary Sciences Water Science and Technology

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