PGE 386 Advanced fluid flow in porous media

The course addresses various approaches taken for modeling the flow of fluids in porous media. The following topics are covered in detail.

  • Elementary petrophysical properties of porous media.
  • Continuum models for single-phase flow. Darcy's law and conservation equations
  • Models for single phase flow in porous media
  • Navier-Stokes equations and Darcy's law. Introduction to averaging techniques. “Flow through” and “flow over” models.
  • Flow in anisotropic / heterogeneous media.
  • Geostatistical representations of heterogeneity.
  • Multiphase flow in porous media: A continuum approach.
  • Capillary pressure and relative permeability concepts
  • Solution of initial and boundary value problems.
  • The nature of residual wetting and non-wetting phases.
  • Multiphase flow in heterogeneous porous media.
  • Empirical models for two and three phase relative permeability.
  • Network models for immiscible two-phase flow. Estimation of relative permeabilities, capillary pressure curves and dispersion coefficients using network models.
  • Percolation theory
  • Effective Medium models
  • Up-scaling issues in flow problems in porous media
  • Multi-component, multi-phase flow.
  • Special Topics (if time permits)
  • Non-Darcy flow
  • Oscillatory flow, dynamic permeability.
  • Coupled processes: Electrochemical and streaming potentials
  • Flow of colloidal suspensions

COURSE SUMMARY

Week 1 Introduction to the course. Porosity. Continuum models to describe single phase flow through porous media.
Week 2 Microscopic models for single-phase flow, phenomenological models, conduit models, cell models, etc.
Week 3 Single phase flow in anisotropic / heterogeneous porous media.
Week 4 Capillarity and surface tension. A classical view of two-phase flow (capillary pressure and relative permeability curves).
Week 5 Solution of initial and boundary value problems.
Week 6 Empirical models for two and three phase relative permeability.
Week 7 The nature of residual saturations.
Week 8 Percolation theory / Effective Medium Theory, application to estimating kr, Pc–Sw curves.
Week 9 Wettability and its impact on fluid flow and trapping.
Week 10 Multi-phase flow in heterogeneous porous media.
Week 11 Multi-component, multi-phase flow
Week 12 Up-scaling issues in flow problems in porous media.
Week 13 Special Topics: Non-Darcy Flow, oscillatory flow (dynamic permeability), residual saturations, ion transport in microporous media, other topics of special interest to the class.
Week 14 Course Review

Texts and other reading:

  1. A set of notes provided by the instructor will form the text for the course.
  2. "Porous Media - Fluid Transport and Pore Structure," F.A.L. Dullien, Acad. Press (1979)
  3. "The Physics of Flow through Porous Media," A. E. Scheidegger, Univ. of Toronto Press (1960)
  4. "Dynamics of Fluids in Porous Media," J. Bear, American Elsevier Pub. (1972)
  5. "Transport Phenomena," Bird, Stewart and Lightfoot, Wiley Pub. (1960)