Abstract
The main purpose of this thesis has been to analyse self-adjoint second order elliptic partial differential equations arising in reservoir simulation. It studies several mathematical and numerical problems for the pressure equation arising in models of fluid flow in porous media. The theoretical results obtained have been illustrated by a series of numerical experiments. The influence of large variations in the mobility tensor upon the solution of the pressure equation is analysed. The performance of numerical methods applied to such problems have been studied. A new upscaling technique for one-phase flow in heterogeneous reservoirs is developed. The stability of the solution of the pressure equation with respect to small perturbations of the mobility tensor is studied. The results are used to develop a new numerical method for a model of fully nonlinear water waves. 158 refs, 39 figs., 12 tabs.
Citation Formats
Nielsen, Bjoern Fredrik.
The pressure equation arising in reservoir simulation. Mathematical properties, numerical methods and upscaling.
Norway: N. p.,
1997.
Web.
Nielsen, Bjoern Fredrik.
The pressure equation arising in reservoir simulation. Mathematical properties, numerical methods and upscaling.
Norway.
Nielsen, Bjoern Fredrik.
1997.
"The pressure equation arising in reservoir simulation. Mathematical properties, numerical methods and upscaling."
Norway.
@misc{etde_328123,
title = {The pressure equation arising in reservoir simulation. Mathematical properties, numerical methods and upscaling}
author = {Nielsen, Bjoern Fredrik}
abstractNote = {The main purpose of this thesis has been to analyse self-adjoint second order elliptic partial differential equations arising in reservoir simulation. It studies several mathematical and numerical problems for the pressure equation arising in models of fluid flow in porous media. The theoretical results obtained have been illustrated by a series of numerical experiments. The influence of large variations in the mobility tensor upon the solution of the pressure equation is analysed. The performance of numerical methods applied to such problems have been studied. A new upscaling technique for one-phase flow in heterogeneous reservoirs is developed. The stability of the solution of the pressure equation with respect to small perturbations of the mobility tensor is studied. The results are used to develop a new numerical method for a model of fully nonlinear water waves. 158 refs, 39 figs., 12 tabs.}
place = {Norway}
year = {1997}
month = {Dec}
}
title = {The pressure equation arising in reservoir simulation. Mathematical properties, numerical methods and upscaling}
author = {Nielsen, Bjoern Fredrik}
abstractNote = {The main purpose of this thesis has been to analyse self-adjoint second order elliptic partial differential equations arising in reservoir simulation. It studies several mathematical and numerical problems for the pressure equation arising in models of fluid flow in porous media. The theoretical results obtained have been illustrated by a series of numerical experiments. The influence of large variations in the mobility tensor upon the solution of the pressure equation is analysed. The performance of numerical methods applied to such problems have been studied. A new upscaling technique for one-phase flow in heterogeneous reservoirs is developed. The stability of the solution of the pressure equation with respect to small perturbations of the mobility tensor is studied. The results are used to develop a new numerical method for a model of fully nonlinear water waves. 158 refs, 39 figs., 12 tabs.}
place = {Norway}
year = {1997}
month = {Dec}
}