Abstract
The thesis is concerned with numerically simulating multicomponent, multiphase, reactive transport in heterogeneous porous medium. Such processes are ubiquitous, for example, deposition of green house gases, flow of hydrocarbons and groundwater remediation. Understanding such processes is important from social and economic point of view. For the success of geological sequestration, an accurate estimation of migration patterns of green-house gases is essential. Due to an ever increasing computer power, computational mathematics has become an important tool for predicting dynamics of porous media fluids. Numerical and mathematical modelling of processes in a domain requires grid generation in the domain, discretization of the continuum equations on the generated grid, solution of the formed linear or nonlinear system of discrete equations and finally visualization of the results. The thesis is composed of three chapters and eight papers. Chapter 2 presents two techniques for generating structured quadrilateral and hexahedral meshes. These techniques are called algebraic and elliptic methods. Algebraic techniques are by far the most simple and computationally efficient method for grid generation. Transfinite interpolation operators are a kind of algebraic grid generation technique. In this chapter, many transfinite interpolation operators for grid generation are derived from 1D projection operators. In this chapter, some important
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Citation Formats
Khattri, Sanjay Kumar.
Numerical Tools for Multicomponent, Multiphase, Reactive Processes: Flow of CO{sub 2} in Porous Medium.
Norway: N. p.,
2006.
Web.
Khattri, Sanjay Kumar.
Numerical Tools for Multicomponent, Multiphase, Reactive Processes: Flow of CO{sub 2} in Porous Medium.
Norway.
Khattri, Sanjay Kumar.
2006.
"Numerical Tools for Multicomponent, Multiphase, Reactive Processes: Flow of CO{sub 2} in Porous Medium."
Norway.
@misc{etde_20805443,
title = {Numerical Tools for Multicomponent, Multiphase, Reactive Processes: Flow of CO{sub 2} in Porous Medium}
author = {Khattri, Sanjay Kumar}
abstractNote = {The thesis is concerned with numerically simulating multicomponent, multiphase, reactive transport in heterogeneous porous medium. Such processes are ubiquitous, for example, deposition of green house gases, flow of hydrocarbons and groundwater remediation. Understanding such processes is important from social and economic point of view. For the success of geological sequestration, an accurate estimation of migration patterns of green-house gases is essential. Due to an ever increasing computer power, computational mathematics has become an important tool for predicting dynamics of porous media fluids. Numerical and mathematical modelling of processes in a domain requires grid generation in the domain, discretization of the continuum equations on the generated grid, solution of the formed linear or nonlinear system of discrete equations and finally visualization of the results. The thesis is composed of three chapters and eight papers. Chapter 2 presents two techniques for generating structured quadrilateral and hexahedral meshes. These techniques are called algebraic and elliptic methods. Algebraic techniques are by far the most simple and computationally efficient method for grid generation. Transfinite interpolation operators are a kind of algebraic grid generation technique. In this chapter, many transfinite interpolation operators for grid generation are derived from 1D projection operators. In this chapter, some important properties of hexahedral elements are also mentioned. These properties are useful in discretization of partial differential equations on hexahedral mesh, improving quality of the hexahedral mesh, mesh generation and visualization. Chapter 3 is about CO{sub 2} flow in porous media. In this chapter, we present the mathematical models and their discretization for capturing major physical processes associated with CO{sub 2} deposition in geological formations. Some important simulations of practical applications in 2D and 3D are presented. Chapter 4 presents Control Volume discretization on adaptive meshes. In this chapter, criteria for adaptive refinement and an adaptive algorithm is presented. The following papers are included in Part II Paper A: A New Smoothing Algorithm for Quadrilateral and Hexahedral Meshes presents an alternative to the Laplacian smoothing. The new smoothing is called the parallelogram smoothing. Parallelogram smoothing tries to fit a domain with the best possible parallelograms or parallelepipeds. Since many numerical methods in porous media flow such as the well known MPFA produces a symmetric system on parallelogram meshes. So, the parallelogram smoothing can be useful for porous media flow simulations. Error of streamline methods on parallelogram and parallelopiped mesh is minimum. Paper B: Hexahedral Mesh by Area Functional. We review the Area functional for generating hexahedral meshes. An algorithm for optimization of the area functional is presented. Since a global optimization can be computationally expensive, it is shown that such an optimization can be applied locally. Paper C: An Effective Quadrilateral Mesh Adaptation Paper is about generating adaptive quadrilateral meshes. We present an extension of the Area functional for generating adaptive meshes. Several numerical examples are reported for showing effectiveness of the functional. Generally for quadrilateral mesh adaptation, we solve a coupled system of non-linear partial differential equations such as the well known non-linear elliptic system. Presented new idea is simple and computationally efficient. The other big plus of the method is that even after generating the solution adapted grid, the cells remain convex. Paper D: Deposition of Green House Gases by Compositional Simulator: Long Term Reactive Transport of CO{sub 2} in the Sand of Utsira In this work, we present the mathematical models and their discretization for capturing major physical processes associated with CO{sub 2} sequestration/deposition in a porous medium. We verify our simulator by comparing our results against available results. We analyze impact of fluid movement on long term CO{sub 2} migration at the Utsira. We analyze how flow of medium fluids affects important parameters such as the pH and evolution of CO{sub 2} saturation. The author's contributions to the paper include mesh generation in the Utsira formation, development of geometrical and lithological models, coupling of the Accrete and Athena code. Paper E: Control Volume Finite Difference On Adaptive Meshes. It is shown that discrete system formed on the adaptive meshes is not only more accurate but are also well conditioned compared to the one formed on the uniform meshes. Paper F: Grid Generation and Adaptation by Functionals Paper reviews various functionals for grid generation and adaptation. It is a well known fact that accuracy of a numerical simulation and quality of the grid are strongly related. In this article, we review various functionals for generating high quality structured quadrilateral meshes in two dimensional domains. Analysis of Winslow and Modified Liao functionals are presented. Numerical experiments are also reported to support our theoretical analysis. We demonstrate use of the Area functional for generating adaptive quadrilateral meshes. Paper G: CO{sub 2} storage in the Utsira Formation-ATHENA 3D reactive transport simulations Article presents 3D simulation of CO{sub 2} sequestration/deposition at the Utsira formation. Our model consists of fourteen chemical and sixteen mineral species. We present 1000 years simulation of CO{sub 2} deposition. In this work, the author prepared the geometrical model of the Utsira formation. He coupled the ACCRETE geochemistry module and the Athena simulator. Paper H: Numerical convergence on adaptive grids for control volume methods The article presents convergence of the Finite Volume Method on uniform and adaptive meshes. We also analyse convergence of the method in various norms on uniform meshes for problems with regularity.}
place = {Norway}
year = {2006}
month = {Jul}
}
title = {Numerical Tools for Multicomponent, Multiphase, Reactive Processes: Flow of CO{sub 2} in Porous Medium}
author = {Khattri, Sanjay Kumar}
abstractNote = {The thesis is concerned with numerically simulating multicomponent, multiphase, reactive transport in heterogeneous porous medium. Such processes are ubiquitous, for example, deposition of green house gases, flow of hydrocarbons and groundwater remediation. Understanding such processes is important from social and economic point of view. For the success of geological sequestration, an accurate estimation of migration patterns of green-house gases is essential. Due to an ever increasing computer power, computational mathematics has become an important tool for predicting dynamics of porous media fluids. Numerical and mathematical modelling of processes in a domain requires grid generation in the domain, discretization of the continuum equations on the generated grid, solution of the formed linear or nonlinear system of discrete equations and finally visualization of the results. The thesis is composed of three chapters and eight papers. Chapter 2 presents two techniques for generating structured quadrilateral and hexahedral meshes. These techniques are called algebraic and elliptic methods. Algebraic techniques are by far the most simple and computationally efficient method for grid generation. Transfinite interpolation operators are a kind of algebraic grid generation technique. In this chapter, many transfinite interpolation operators for grid generation are derived from 1D projection operators. In this chapter, some important properties of hexahedral elements are also mentioned. These properties are useful in discretization of partial differential equations on hexahedral mesh, improving quality of the hexahedral mesh, mesh generation and visualization. Chapter 3 is about CO{sub 2} flow in porous media. In this chapter, we present the mathematical models and their discretization for capturing major physical processes associated with CO{sub 2} deposition in geological formations. Some important simulations of practical applications in 2D and 3D are presented. Chapter 4 presents Control Volume discretization on adaptive meshes. In this chapter, criteria for adaptive refinement and an adaptive algorithm is presented. The following papers are included in Part II Paper A: A New Smoothing Algorithm for Quadrilateral and Hexahedral Meshes presents an alternative to the Laplacian smoothing. The new smoothing is called the parallelogram smoothing. Parallelogram smoothing tries to fit a domain with the best possible parallelograms or parallelepipeds. Since many numerical methods in porous media flow such as the well known MPFA produces a symmetric system on parallelogram meshes. So, the parallelogram smoothing can be useful for porous media flow simulations. Error of streamline methods on parallelogram and parallelopiped mesh is minimum. Paper B: Hexahedral Mesh by Area Functional. We review the Area functional for generating hexahedral meshes. An algorithm for optimization of the area functional is presented. Since a global optimization can be computationally expensive, it is shown that such an optimization can be applied locally. Paper C: An Effective Quadrilateral Mesh Adaptation Paper is about generating adaptive quadrilateral meshes. We present an extension of the Area functional for generating adaptive meshes. Several numerical examples are reported for showing effectiveness of the functional. Generally for quadrilateral mesh adaptation, we solve a coupled system of non-linear partial differential equations such as the well known non-linear elliptic system. Presented new idea is simple and computationally efficient. The other big plus of the method is that even after generating the solution adapted grid, the cells remain convex. Paper D: Deposition of Green House Gases by Compositional Simulator: Long Term Reactive Transport of CO{sub 2} in the Sand of Utsira In this work, we present the mathematical models and their discretization for capturing major physical processes associated with CO{sub 2} sequestration/deposition in a porous medium. We verify our simulator by comparing our results against available results. We analyze impact of fluid movement on long term CO{sub 2} migration at the Utsira. We analyze how flow of medium fluids affects important parameters such as the pH and evolution of CO{sub 2} saturation. The author's contributions to the paper include mesh generation in the Utsira formation, development of geometrical and lithological models, coupling of the Accrete and Athena code. Paper E: Control Volume Finite Difference On Adaptive Meshes. It is shown that discrete system formed on the adaptive meshes is not only more accurate but are also well conditioned compared to the one formed on the uniform meshes. Paper F: Grid Generation and Adaptation by Functionals Paper reviews various functionals for grid generation and adaptation. It is a well known fact that accuracy of a numerical simulation and quality of the grid are strongly related. In this article, we review various functionals for generating high quality structured quadrilateral meshes in two dimensional domains. Analysis of Winslow and Modified Liao functionals are presented. Numerical experiments are also reported to support our theoretical analysis. We demonstrate use of the Area functional for generating adaptive quadrilateral meshes. Paper G: CO{sub 2} storage in the Utsira Formation-ATHENA 3D reactive transport simulations Article presents 3D simulation of CO{sub 2} sequestration/deposition at the Utsira formation. Our model consists of fourteen chemical and sixteen mineral species. We present 1000 years simulation of CO{sub 2} deposition. In this work, the author prepared the geometrical model of the Utsira formation. He coupled the ACCRETE geochemistry module and the Athena simulator. Paper H: Numerical convergence on adaptive grids for control volume methods The article presents convergence of the Finite Volume Method on uniform and adaptive meshes. We also analyse convergence of the method in various norms on uniform meshes for problems with regularity.}
place = {Norway}
year = {2006}
month = {Jul}
}