From discrete to continuum concepts of flow in fractured porous media

Abstract

As more and more engineering applications require the correct simulation of flow and transport processes in porous media, and while many of these media present a certain degree of fracturing, this work deals with the development of numerical models that can simulate two-phase flow in large-scale fractured reservoirs. Among the applications which these models are addressing to, there are the estimation of contaminant spreading and removal, the reservoir exploitation, or more recently the CO2 sequestration, the geothermal reservoir exploitation, and the nuclear waste repositories. Fractured systems are ubiquitous around the world and can occur on avariety of lengths and scales which makes difficult the development of a general model that can handle easily all of them. The overall purpose of this work is to improve the understanding over the concepts of the multiphase flow and processes in the fractured porous media and develop a conceptual model that allows the study of two-phase flow in fractures of arbitrary size, orientation and shape. The flow models have been roughly classified in discrete fracturemodels (DFM), continuum fracturemodels (CFM) and hybrid. The DFMs consider the fractures explicitly and thereforerequirehuge computation power,whereas CFMs require the determination of arepresentative elementary volume (REV), the appropriate effective parameters and transfer functions between continua. For alarge scale problem, like aCO2 storage reservoir,there can be millions of fractures which might have to be considered and could be a formidable task for a DFM simulator.In this sense a continuum model, which is in this case in the form of a generalized dual-porosity representation, does not require the fine discretization of a DFM and the detailed fracturecharacterization during simulations. Thus, another goal of this work is to build areliable large scale multiphase flow simulator based on the continuum approach. Two flow simulators, 2pDFM and 2pMINC,have been developed and tested based on the two different fracture model concepts. Both simulators are implemented in the numerical toolbox DuMux.The 2pDFM model simulates the two-phase flow in fractured porous media using aDFM approach, with a lower dimensional representation for the fracture network (DFM-L). The model is capable to account for storage in the fractures. The 2pMINC model simulates two-phase flow in fractured porous media using the multiple interacting continua (MINC) method with an improved upscaling technique. The complex transient behavior of the flow processes in fractured porous media is captured by subgridding the coarse blocks in nested volume elements which have effective properties calculated from the detailed representation of the fracturesystem. In this way,the physically based approach is kept, the accuracy of the model is preserved ,the common use of empirically derived transfer functions is avoided and the complexity of the problem is considerably reduced which is reflected in the speedup factors up to 1000. This research extends the applicability range of the upscaling procedure to include entry pressure effects. Moreover,a general workflow has been developed for the numerical simulation of the two-phase flow in large-scale fractured porous media. The results are verified, validated and tested in a fully comprehensive way for both models. To test the behaviour of the simulator for field scale problems they are applied to an idealized medium with periodic fracture pattern and to areal, naturally fractured reservoir from the Bristol Channel. The evaluation shows that the extended MINC model is able to reproduce both, the large-scale permeability and the dynamics of the fracture-matrix mass transfer,correctly. The extended MINC method and the simulation procedure is flexible as it allows choosing the accuracy of the solution, the computation speed, and allows working with spatial information about the fracture system of various complexity and detail.

Kluftsysteme sind auf dieser Welt allgegenwärtig und werden seit mehr als 60 Jahren in unterschiedlichen Bereichen, wie der Hydrologie, der Erdölförderung oder der geothermalen Energie untersucht. Für eine Vielzahl von Anwendungsbereichen sind prädiktive Simulationen der Mehr-phasenströmung und des Transports in geklüfteten porösen Medien von großem Interesse, z.B. bei der Erschließung von Wasserspeichern zur Wasserversorgung, bei der Sanierung wasserführender Schichten (Aquifere) (Berkowitz [2002],Niessner et al.[2005]), bei der Erschließung von Erdölspeichern (Lemonnier and Bourbiaux [2010], Kazemi [1976]), bei der Erschließung geothermaler Speicher,der Wärmespeicherung, bei Prozessen in Bergbau und Mineralisierung (lokale Extraktion und Bestimmung von Erzvorkommen), bei der CO2 Speicherung in geologischen Schichten (Carneiro [2009], Kopp [2009]), bei der Atommülllagerung (Bodvarsson et al. [1999], Reichenberger et al. [2003]) usw.. All diese Anwendungen können mittels Gestaltung und Überwachung durch Computermodelle besser verstanden werden. Rechnergestützte Modellierung ist der Prozess der Entwicklung mathematischer Repräsentationen einer echten oder hypothetischen Situation, um diese besser zu untersuchen, und um einen Einblick in die Funktionsweise und Handhabung dieser Systeme zu erhalten. Im Falle der Endlagerung radioaktiven Mülls müssen die unterirdischen Anlagen eine Sicherheitsgarantie von hunderten oder gar tausenden von Jahren bieten. Daher liegt der Schlüssel zum Verständnis mehrphasiger Prozesse und zur Vorhersage über das Verhalten des Reservoirs in der Erstellung eines genauen Modells. Einige der größten Herausforderungen bei der Erstellung von Mehrphasen-Strömungsmodellen in geklüfteten porösen Medien stellen die großen Unterschiede der Klufteigenschaften und der Eigenschaften des umgebenden Gesteins, sowie die unterschiedlichen Zeitmaßstäbe der Strömungsprozesse dar. In dieser Arbeit werden mathematische Modelle und numerische Simulationswerkzeuge für geklüftete poröse Medien entwickelt, die eine wichtige Rolle bei der Untersuchung unterirdischer Reservoirs, bei der Gestaltung und Untersuchung von Feldversuchen und bei der Verbesserung und Optimierung der Handhabung geologischer Reservoirespielen.