Title page for ETD etd-11072011-084037

Type of Document Dissertation
Author Lane, Nathan Matthew
Author's Email Address nlane4@tigers.lsu.edu, NathanLane@bp.com
URN etd-11072011-084037
Title Numerical Studies of Flow in Porous Media Using an Unstructured Approach
Degree Doctor of Philosophy (Ph.D.)
Department Chemical Engineering
Advisory Committee
Advisor Name Title
Thompson, Karsten E. Committee Chair
White, Christopher Committee Co-Chair
Dooley, Kerry M. Committee Member
Pike, Ralph W. Committee Member
Spivak, David Dean's Representative
  • pore-scale modeling
  • image-based modeling
  • unstructured meshing
  • finite element method
  • permeability
  • tortuosity
Date of Defense 2011-08-22
Availability unrestricted
Flow and transport in porous media is relevant to many areas of engineering and science including groundwater hydrology and the recovery of oil and gas. Porous materials are characterized by the unique shape and connectivity of the internal void structures which give rise to a large range in macroscopic transport properties. Historically an inability to accurately describe the internal pore-structure has prevented detailed study of the role of pore structure on transport. In recent decades however, the combination of high resolution imaging technologies with computational modeling has seen the development of fundamental pore-scale techniques for studying flow in porous media.

Image-based pore-scale modeling of transport phenomena has become an important tool for understanding the complicated relationships between pore structure and measurable macroscopic properties, including permeability and formation factor. This has commonly been achieved by a network-based approach where the pore space is idealized as a series of pores connected by throats, or by a grid-based approach where the voxels of a 3D image represent structured quadrilateral elements or nodal locations. In this work however, image-based unstructured meshing techniques are used to represent voxelised pore spaces by grids comprising entirely of tetrahedral elements. These unstructured tetrahedral grids are used in finite element models to calculate permeability and formation factor.

Solutions to the Stokes equations governing creeping, or Darcy flow, are used to validate the finite element approach employed in this work, and to assess the impact of different image-based unstructured meshing strategies on predicted permeability. Testing shows that solutions to the Stokes equations by a P2P1 tetrahedral element are significantly more accurate than solutions based on a P1P1 element, while permeability is shown to be sensitive to structural changes to the pore space induced by different meshing approaches. The modeling approach is also used to investigate the relationship of an electric and hydraulic definition of tortuosity to the Carman-Kozeny equation. The results of simulations using a number of computer generated porous structures indicate that an electrical tortuosity based on computed formation factor is well correlated with the tortuosity suggested by the Carman-Kozeny equation.

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