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