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The coupling between subsurface flow and reservoir geomechanics plays a critical role in obtaining accurate results for models involving reservoir deformation, surface subsidence, well stability, sand production, waste deposition, hydraulic fracturing, CO2 sequestration, and hydrocarbon recovery. From a pure computational point of view, such a coupling can be quite a challenging and complicated task. This stems from the fact that the constitutive equations governing geomechanical deformations are different in nature from those governing porous media flow. The geomechanical effects account for the influence of deformations in the porous media caused due to the pore pressure and can be very important especially in the case of stress-sensitive and fractured reservoirs. Considering that fractures are very much prevalent in the porous media and they have strong influence on the flow profiles, it is important to study coupled geomechanics and flow problems in fractured reservoirs. In this work, we pursue three main objectives: first, to rigorously design and analyze iterative and explicit coupling algorithms for coupling flow and geomechanics in both poro-elasitc and fractured poro-elastic reservoirs. The analysis of iterative coupling schemes relies on studying the equations satisfied by the difference of iterates and using a Banach contraction argument to derive geometric convergence (Banach fixed-point contraction) results. The analysis of explicit coupling schemes result in analogous stability estimates. In this work, conformal Galerkin is used for mechanics, and a mixed formulation, including the Multipoint Flux Mixed Finite Element method as a special case, is used for the flow model. For fractured poro-elastic media, our iteratively coupled schemes are adaptations, due to the presence of fractures, of the classical fixed stress-splitting scheme, in which fractures are treated as possibly non-planar interfaces. The second main objective in this work is to exploit the different time scales of the mechanics and flow problems. Due to its physical nature, the geomechanics problem can cope with a coarser time step compared to the flow problem. This makes the multirate coupling scheme, the one in which the flow problem takes several (finer) time steps within the same coarse mechanics time step, a natural candidate in this setting. Inspired by that, we rigorously formulate and analyze convergence properties of both multirate iterative and explicit coupling schemes in both poro-elastic and fractured poro-elastic reservoirs. In addition, our theoretically derived Banach contraction estimates are validated against numerical simulations. The third objective in this work is to optimize the solution strategy of the nonlinear flow model in coupled flow and mechanics schemes. The global inexact Newton method, combined with the line search backtracking algorithm along with heuristic forcing functions, can be efficiently employed to reduce the number of flow linear iterations, and hence, the overall CPU run time. We first validate these computational savings for challenging two-phase benchmark problems including the full SPE10 model. Motivated by the obtained results, we incorporate this strategy as a nonlinear solver framework to solve the nonlinear flow problem in multirate iteratively coupled schemes. This leads to a scheme that reduces both the number of flow and mechanics linear iterations efficiently. All our numerical implementations in this work are built on top of our in-house reservoir simulator (IPARS).
This book provides a systematic treatment of the geometrical and transport properties of fractures, fracture networks, and fractured porous media. It is divided into two major parts. The first part deals with geometry of individual fractures and of fracture networks. The use of the dimensionless density rationalizes the results for the percolation threshold of the networks. It presents the crucial advantage of grouping the numerical data for various fracture shapes. The second part deals mainly with permeability under steady conditions of fractures, fracture networks, and fractured porous media. Again the results for various types of networks can be rationalized by means of the dimensionless density. A chapter is dedicated to two phase flow in fractured porous media.
The supply and protection of groundwater, the production of hydrocarbon reservoirs, land subsidence in coastal areas, exploitation of geothermal energy, the long-term disposal of critical wastes ... What do these issues have in common besides their high socio-economic impact? They are all closely related to fluid flow in porous and/or fractured rock. As the conditions of fluid flow in many cases depend on the mechanical behavior of rocks, coupling between the liquid phase and the rock matrix can generally not be neglected. For the past five years or so, studies of rock physics and rock mechanics linked to coupling phenomena have received increased attention. In recognition of this, a Euroconference on thermo-hydro-mechanical coupling in fractured rock was held at Bad Honnef, Germany, in November 2000. Most of the twenty papers collected in this volume were presented at this meeting. The contributions lead to deeper insight in processes where such coupling is relevant.
This text features 105 papers dealing with the fundamentals and the applications of poromechanics from the Biot conference of 1998, held in Louvain-la-Neuve. Topics include: wave propogation; numerical modelling; identification of poromechanical parameters; and constitutive modelling.
Scientific understanding of fluid flow in rock fracturesâ€"a process underlying contemporary earth science problems from the search for petroleum to the controversy over nuclear waste storageâ€"has grown significantly in the past 20 years. This volume presents a comprehensive report on the state of the field, with an interdisciplinary viewpoint, case studies of fracture sites, illustrations, conclusions, and research recommendations. The book addresses these questions: How can fractures that are significant hydraulic conductors be identified, located, and characterized? How do flow and transport occur in fracture systems? How can changes in fracture systems be predicted and controlled? Among other topics, the committee provides a geomechanical understanding of fracture formation, reviews methods for detecting subsurface fractures, and looks at the use of hydraulic and tracer tests to investigate fluid flow. The volume examines the state of conceptual and mathematical modeling, and it provides a useful framework for understanding the complexity of fracture changes that occur during fluid pumping and other engineering practices. With a practical and multidisciplinary outlook, this volume will be welcomed by geologists, petroleum geologists, geoengineers, geophysicists, hydrologists, researchers, educators and students in these fields, and public officials involved in geological projects.
Sixty-five papers cover a wide range of topics from engineering applications to theoretical developments in the areas of embankment and slope stability, underground cavity design and mining; dynamic analysis, soil and structure interaction, and coupled processes and fluid flow.
This book focuses on the implementation and application of new concepts and methods to modelling, analysis, building, performance control and repair of structures of and in jointed rock and rock masses. It provides a forum for presentation of new research results and discussion for researchers.