Title page for ETD etd-07012008-115136


Type of Document Dissertation
Author Lee, Im Soo
Author's Email Address ilee@vt.edu
URN etd-07012008-115136
Title Computational Techniques for Efficient Solution of Discretized Biot’s Theory for Fluid Flow in Deformable Porous Media
Degree PhD
Department Civil Engineering
Advisory Committee
Advisor Name Title
Gutierrez, Marte S. Committee Chair
Chin, Lee Committee Member
Duncan, James Michael Committee Member
Filz, George M. Committee Member
Keywords
  • Biot’s theory
  • fully-coupled solution
  • finite elements
Date of Defense 2008-06-24
Availability unrestricted
Abstract
In soil and rock mechanics, coupling effects between geomechanics field and fluid-flow field are important to understand many physical phenomena. Coupling effects in fluid-saturated porous media comes from the interaction between the geomechanics field and the fluid flow. Stresses subjected on the porous material result volumetric strains and fluid diffusion in the pores. In turn, pore pressure change cause effective stresses change that leads to the deformation of the geomechanics field. Coupling effects have been neglected in traditional geotechnical engineering and petroleum engineering however, it should not be ignored or simplified to increases reliability of the results. The coupling effect in porous media was theoretically established in the poroelasticity theory developed by Biot, and it has become a powerful theory for modeling three-dimensional consolidation type of problem.

The analysis of the porous media with fully-coupled simulations based on the Biot’s theory requires intensive computational effort due to the large number of interacting fields. Therefore, advanced computational techniques need to be exploited to reduce computational time. In order to solve the coupled problem, several techniques are currently available such as one-way coupling, partial-coupling, and full-coupling. The fully-coupled approach is the most rigorous approach and produces the most correct results. However, it needs large computational efforts because it solves the geomechanics and the fluid-flow unknowns simultaneously and monolithically. In order to overcome this limitation, staggered solution based on the Biot’s theory is proposed and implemented using a modular approach. In this thesis, Biot’s equations are implemented using a Finite Element method and/or Finite Difference method with expansion of nonlinear stress-strain constitutive relation and multi-phase fluid flow. Fully-coupled effects are achieved by updating the compressibility matrix and by using an additional source term in the conventional fluid flow equation. The proposed method is tested in multi-phase FE and FD fluid flow codes coupled with a FE geomechanical code and numerical results are compared with analytical solutions and published results.

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