## Abstract

The thesis is divided into two main parts. Part I gives an overview and summary of the theory that lies behind the flow equations and the discretization principles used in the work. Part II is a collection of research papers that have been written by the candidate (in collaboration with others). The main objective of this thesis is the discretization of an elliptic PDE which describes the pressure in a porous medium. The porous medium will in general be described by permeability tensors which are heterogeneous and anisotropic. In addition, the geometry is often complex for practical applications. This requires discretization approaches that are suited for the problems in mind. The discretization approaches used here are based on imposed flux and potential continuity, and will be discussed in detail in Chapter 3 of Part I. These methods are called Multi Point Flux Approximation Methods, and the acronym MPFA will be used for them. Issues related to these methods will be the main issue of this thesis. The rest of this thesis is organised as follows: Part I: Chapter 1 gives a brief overview of the physics and mathematics behind reservoir simulation. The standard mass balance equations are presented, and we
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## Citation Formats

Eigestad, Geir Terje.
Reservoir simulation with imposed flux continuity conditions on heterogeneous and anisotropic media for general geometries, and the inclusion of hysteresis in forward modeling.
Norway: N. p.,
2003.
Web.

Eigestad, Geir Terje.
Reservoir simulation with imposed flux continuity conditions on heterogeneous and anisotropic media for general geometries, and the inclusion of hysteresis in forward modeling.
Norway.

Eigestad, Geir Terje.
2003.
"Reservoir simulation with imposed flux continuity conditions on heterogeneous and anisotropic media for general geometries, and the inclusion of hysteresis in forward modeling."
Norway.

@misc{etde_20662615,

title = {Reservoir simulation with imposed flux continuity conditions on heterogeneous and anisotropic media for general geometries, and the inclusion of hysteresis in forward modeling}

author = {Eigestad, Geir Terje}

abstractNote = {The thesis is divided into two main parts. Part I gives an overview and summary of the theory that lies behind the flow equations and the discretization principles used in the work. Part II is a collection of research papers that have been written by the candidate (in collaboration with others). The main objective of this thesis is the discretization of an elliptic PDE which describes the pressure in a porous medium. The porous medium will in general be described by permeability tensors which are heterogeneous and anisotropic. In addition, the geometry is often complex for practical applications. This requires discretization approaches that are suited for the problems in mind. The discretization approaches used here are based on imposed flux and potential continuity, and will be discussed in detail in Chapter 3 of Part I. These methods are called Multi Point Flux Approximation Methods, and the acronym MPFA will be used for them. Issues related to these methods will be the main issue of this thesis. The rest of this thesis is organised as follows: Part I: Chapter 1 gives a brief overview of the physics and mathematics behind reservoir simulation. The standard mass balance equations are presented, and we try to explain what reservoir simulation is. Some standard discretization s methods are briefly discussed in Chapter 2. The main focus in Part I is on the MPFA discretization approach for various geometries, and is given in Chapter 3. Some details may have been left out in the papers of Part II, and the section serves both as a summary of the discretization method(s), as well as a more detailed description than what is found in the papers. In Chapter 4, extensions to handle time dependent and nonlinear problems are discussed. Some of the numerical examples presented in Part II deal with two phase flow, and are based on the extension given in this chapter. Chapter 5 discusses numerical results that have been obtained for the MPFA methods for elliptic problems, and Chapter 6 deals with issues related to properties of the discrete set of (one phase) pressure equations. Chapter 7 contains summaries of the research papers found in Part II.}

place = {Norway}

year = {2003}

month = {Apr}

}

title = {Reservoir simulation with imposed flux continuity conditions on heterogeneous and anisotropic media for general geometries, and the inclusion of hysteresis in forward modeling}

author = {Eigestad, Geir Terje}

abstractNote = {The thesis is divided into two main parts. Part I gives an overview and summary of the theory that lies behind the flow equations and the discretization principles used in the work. Part II is a collection of research papers that have been written by the candidate (in collaboration with others). The main objective of this thesis is the discretization of an elliptic PDE which describes the pressure in a porous medium. The porous medium will in general be described by permeability tensors which are heterogeneous and anisotropic. In addition, the geometry is often complex for practical applications. This requires discretization approaches that are suited for the problems in mind. The discretization approaches used here are based on imposed flux and potential continuity, and will be discussed in detail in Chapter 3 of Part I. These methods are called Multi Point Flux Approximation Methods, and the acronym MPFA will be used for them. Issues related to these methods will be the main issue of this thesis. The rest of this thesis is organised as follows: Part I: Chapter 1 gives a brief overview of the physics and mathematics behind reservoir simulation. The standard mass balance equations are presented, and we try to explain what reservoir simulation is. Some standard discretization s methods are briefly discussed in Chapter 2. The main focus in Part I is on the MPFA discretization approach for various geometries, and is given in Chapter 3. Some details may have been left out in the papers of Part II, and the section serves both as a summary of the discretization method(s), as well as a more detailed description than what is found in the papers. In Chapter 4, extensions to handle time dependent and nonlinear problems are discussed. Some of the numerical examples presented in Part II deal with two phase flow, and are based on the extension given in this chapter. Chapter 5 discusses numerical results that have been obtained for the MPFA methods for elliptic problems, and Chapter 6 deals with issues related to properties of the discrete set of (one phase) pressure equations. Chapter 7 contains summaries of the research papers found in Part II.}

place = {Norway}

year = {2003}

month = {Apr}

}