Multiscale Methods For Flow And Transport In Heterogeneous Porous Media
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Multiscale Methods For Flow And Transport In Heterogeneous Porous Media
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Author : Ruben Juanes
language : en
Publisher:
Release Date : 2008
Multiscale Methods For Flow And Transport In Heterogeneous Porous Media written by Ruben Juanes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Special Issue On Multiscale Methods For Flow And Transport In Heterogeneous Porous Media
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Author : Ruben Juanes
language : en
Publisher:
Release Date : 2008
Special Issue On Multiscale Methods For Flow And Transport In Heterogeneous Porous Media written by Ruben Juanes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Multiscale Analysis And Computation For Flows In Heterogeneous Media
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Author :
language : en
Publisher:
Release Date : 2016
Multiscale Analysis And Computation For Flows In Heterogeneous Media written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Our work in this project is aimed at making fundamental advances in multiscale methods for flow and transport in highly heterogeneous porous media. The main thrust of this research is to develop a systematic multiscale analysis and efficient coarse-scale models that can capture global effects and extend existing multiscale approaches to problems with additional physics and uncertainties. A key emphasis is on problems without an apparent scale separation. Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations. These procedures capture the effects of fine-scale permeability variations through the calculation of specialized coarse-scale basis functions. Most of the multiscale techniques presented to date employ localization approximations in the calculation of these basis functions. For some highly correlated (e.g., channelized) formations, however, global effects are important and these may need to be incorporated into the multiscale basis functions. Other challenging issues facing multiscale simulations are the extension of existing multiscale techniques to problems with additional physics, such as compressibility, capillary effects, etc. In our project, we explore the improvement of multiscale methods through the incorporation of additional (single-phase flow) information and the development of a general multiscale framework for flows in the presence of uncertainties, compressible flow and heterogeneous transport, and geomechanics. We have considered (1) adaptive local-global multiscale methods, (2) multiscale methods for the transport equation, (3) operator-based multiscale methods and solvers, (4) multiscale methods in the presence of uncertainties and applications, (5) multiscale finite element methods for high contrast porous media and their generalizations, and (6) multiscale methods for geomechanics. Below, we present a brief overview of each of these contributions.
Multiscale Methods For Flow And Transport In Porous Media
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Author : Ettore Vidotto
language : en
Publisher:
Release Date : 2019
Multiscale Methods For Flow And Transport In Porous Media written by Ettore Vidotto and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
Uncertainty Quantification Using Multiscale Methods For Porous Media Flows
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Author : Paul Francis Dostert
language : en
Publisher:
Release Date : 2010
Uncertainty Quantification Using Multiscale Methods For Porous Media Flows written by Paul Francis Dostert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
In this dissertation we discuss numerical methods used for uncertainty quantification applications to flow in porous media. We consider stochastic flow equations that contain both a spatial and random component which must be resolved in our numerical models. When solving the flow and transport through heterogeneous porous media some type of upscaling or coarsening is needed due to scale disparity. We describe multiscale techniques used for solving the spatial component of the stochastic flow equations. These techniques allow us to simulate the flow and transport processes on the coarse grid and thus reduce the computational cost. Additionally, we discuss techniques to combine multiscale methods with stochastic solution techniques, specifically, polynomial chaos methods and sparse grid collocation methods. We apply the proposed methods to uncertainty quantification problems where the goal is to sample porous media properties given an integrated response. We propose several efficient sampling algorithms based on Langevin diffusion and the Markov chain Monte Carlo method. Analysis and detailed numerical results are presented for applications in multiscale immiscible flow and water infiltration into a porous medium.
Multi Scale Finite Element Approximation For Transport In Heterogeneous Porous Media
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Author :
language : en
Publisher:
Release Date : 2002
Multi Scale Finite Element Approximation For Transport In Heterogeneous Porous Media written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
The main objective of this study is to develop an efficient multiscale coarse grid method which can be used as a competitive algorithm in studying composite materials and flow transport in strongly heterogeneous porous media. On one hand, we have explored the possibility of using adaptive mesh to reduce the modeling error introduced by the traditional moment average technique. On the other hand, we found that in the case of high aspect ratio permeability tensor, the modeling error in ignoring high order moments (3rd order or higher) could be very large. To overcome this difficulty, we have investigated an alternative approach that uses two-scale homogenization analysis to derive a coarse grid model in a systematic way. Finally, we have made some progress in developing numerical methods to solve multiscale nonlinear stochastic partial differential equations by using Wiener-Chaos expansions. These methods will reduce the problem of solving stochastic PDEs to solving a set of deterministic PDEs. This numerical method can be combined with our multiscale computational method, and can be used to compute accurately high order statistical quantities more efficiently than the traditional Monte-Carlo method.
Multiscale Simulation Framework For Coupled Fluid Flow And Mechanical Deformation
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Author :
language : en
Publisher:
Release Date : 2016
Multiscale Simulation Framework For Coupled Fluid Flow And Mechanical Deformation written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Our work in this project is aimed at making fundamental advances in multiscale methods for flow and transport in highly heterogeneous porous media. The main thrust of this research is to develop a systematic multiscale analysis and efficient coarse-scale models that can capture global effects and extend existing multiscale approaches to problems with additional physics and uncertainties. A key emphasis is on problems without an apparent scale separation. Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations. These procedures capture the effects of fine-scale permeability variations through the calculation of specialized coarse-scale basis functions. Most of the multiscale techniques presented to date employ localization approximations in the calculation of these basis functions. For some highly correlated (e.g., channelized) formations, however, global effects are important and these may need to be incorporated into the multiscale basis functions. Other challenging issues facing multiscale simulations are the extension of existing multiscale techniques to problems with additional physics, such as compressibility, capillary effects, etc. In our project, we explore the improvement of multiscale methods through the incorporation of additional (single-phase flow) information and the development of a general multiscale framework for flows in the presence of uncertainties, compressible flow and heterogeneous transport, and geomechanics. We have considered (1) adaptive local-global multiscale methods, (2) multiscale methods for the transport equation, (3) operator-based multiscale methods and solvers, (4) multiscale methods in the presence of uncertainties and applications, (5) multiscale finite element methods for high contrast porous media and their generalizations, and (6) multiscale methods for geomechanics.
Stochastic Models For Flow And Transport In Heterogeneous Porous Media
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Author : Amir Hossein Delgoshaie
language : en
Publisher:
Release Date : 2018
Stochastic Models For Flow And Transport In Heterogeneous Porous Media written by Amir Hossein Delgoshaie and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Modeling flow and transport in porous media is an important part of the decision-making process in managing crucial resources such as underground aquifers and hydrocarbon reservoirs, subsurface disposal of contaminants, and the design of battery systems. The multiscale nature of porous media, the heterogeneity of their properties and the uncertainty of our knowledge of these properties pose significant modeling challenges that have been the focus of extensive research. In this work, four important contributions are made to the modeling of flow and transport in porous systems. First, a non-local formulation is rigorously derived to find the average flow solution in multiscale porous media. Second, the stochastic representation of the flow problem is used for quantifying the flow uncertainty in cases with heterogeneous conductivity fields. An algorithm is proposed for using the Feynman-Kac formulation for one-dimensional elliptic problems with piecewise constant conductivity and various schemes were explored to improve the efficiency of particle tracking algorithms for both stochastic and deterministic flow problems. The third contribution of this work is the introduction of the stencil method, a discrete temporal Markov model for modeling transport in networks representing porous material. The stencil method simplifies the temporal models used to simulate mean transport in porous media. Finally, a fast discrete temporal Markov velocity process is introduced to simulate ensemble transport in highly heterogeneous continuum scale conductivity fields. This is the first stochastic model to simulate dispersion in high-variance conductivity fields for both Gaussian and exponential correlation structures.
Multiscale Mortar Mixed Finite Element Methods For Flow Problems In Highly Heterogeneous Porous Media
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Author : Hailong Xiao
language : en
Publisher:
Release Date : 2013
Multiscale Mortar Mixed Finite Element Methods For Flow Problems In Highly Heterogeneous Porous Media written by Hailong Xiao and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
We use Darcy's law and conservation of mass to model the flow of a fluid through a porous medium. It is a second order elliptic system with a heterogeneous coefficient. We consider the equations written in mixed form. In the heterogeneous case, we define a new multiscale mortar space that incorporates purely local information from homogenization theory to better approximate the solution along the interfaces with just a few degrees of freedom. In the case of a locally periodic heterogeneous coefficient of period epsilon, we prove that the new method achieves both optimal order error estimates in the discretization parameters and good approximation when epsilon is small. Moreover, we present numerical examples to assess its performance when the coefficient is not obviously locally periodic. We show that the new mortar method works well, and better than polynomial mortar spaces. On the other hand, we also propose to use multiscale mortars as a coarse component to construct a two-level preconditioner for the saddle point linear system arising from the fine scale discretization of the mixed finite element system. The two-level preconditioners are constructed based on the interfaces. We propose a framework to define the interpolation operators for the face based two-level preconditioners for different combination of coarse and fine scale mortar spaces for matching and nonmatching grids. In this dissertation, we show that for quasi-homogeneous problems and matching grids, the condition number of the preconditioned interface operator is bounded by (log(H/h))2, which is the same as the traditional two-level preconditioners, for quasi-homogeneous problems. We show several numerical examples to demonstrate that for the strongly heterogeneous porous media, it is often desirable and even necessary to use a higher dimensional coarse mortar space to construct the coarse preconditioner to achieve convergence. We apply our ideas to study slightly compressible single phase and two-phase flow in a porous medium. We find that for the nonlinear single phase problem, the two-level preconditioners could be successfully applied to the symmetrized linear system. For the two-phase problem, using the fine scale, instead of multiscale, velocity solutions from the flow problem can greatly benefit the transport problem.
Computational Methods For Flow And Transport In Porous Media
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Author : J.M. Crolet
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Computational Methods For Flow And Transport In Porous Media written by J.M. Crolet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Science categories.
The first Symposium on Recent Advances in Problems of Flow and Transport in Porous Media was held in Marrakech in June '96 and has provided a focus for the utilization of computer methods for solving the many complex problems encountered in the field of solute transport in porous media. This symposium has been successful in bringing together scientists, physicists, hydrogeologists, researchers in soil and fluid mechanics and engineers involved in this multidisciplinary subject. It is clear that the utilization of computer-based models in this domain is still rapidly expanding and that new and novel solutions are being developed. The contributed papers which form this book reflect the recent advances, in particular with respect to new methods, inverse problems, reactive transport, unsaturated media and upscaling. These have been subdivided into the following sections: I. Numerical methods II. Mass transport and heat transfer III. Comparison with experimentation and simulation of real cases This book contains reviewed articles of the top presentations held during the International Symposium on Computer Methods in Porous Media Engineering which took place in Giens (France) in October 1998. All of the presentations and the optimism shown during the meeting provided further evidence that computer modeling is making remarkable progress and is indeed becoming an essential toolkit in the field of porous media and solute transport. I believe that the content of this book provides evidence of this and furthermore gives a comprehensive review of the theoretical developments and applications.